Generally listed in order from highest power (small steps down from the big three) to lowest power (comparable fluff, far weaker abilities).
The high notes of the cleric class include:
Ability to remove status effects; this is actually one of the hardest things to do without a cleric.
Healing. Typically not really that important and handled with a wand of lesser vigor or wand of cure light wounds between battles.
Buffs. No one does it as well as the cleric, but we’ll definitely expect to see replacements dealing in buffs.
Anti-undead. Other classes can get turn undead, but ultimately turn undead isn’t that great and rebuke undead is only somewhat better. Most campaigns don’t require someone dedicated to dealing with undead.
Mystic melee combatant. Lots of classes do this, too many to mention here, but again, none of them do it as well as the cleric.
Cleric dip – Core
Any character with a single level of cleric can do an excellent job “replacing” cleric, without getting into the game-breaking spells. A single level of cleric is one of the most useful and versatile options available, so it’s still very good, but what I want to highlight here is that anyone with the cleric’s spell list gets to activate wands of cleric spells without Use Magic Device. Since many of the most critical and difficult-to-replace abilities of the cleric revolve around healing status effects, which tend not to care about caster level, using wands can replace the cleric quite well. Plus the domains and aura solidify the character as the sort of divine character that the cleric is supposed to be.
Favored Soul – Complete Divine
The most immediate step down; still plenty powerful, just noticeably less so than cleric is.
The favored soul still has the full cleric list, still gets 9th-level spells, but spontaneous casting (complete with new spells every even level starting at 4th, à la sorcerer) and dual ability score (Wisdom and Charisma are both used for spellcasting). It is therefore very powerful, but substantially less powerful than the cleric.
Also, the favored soul doesn’t get domains or turn/rebuke undead, which are major sources of “add-on” power for the cleric. Unfortunately, between the lack of these things and the lack of Knowledge (religion) as a class skill,1 it’s very difficult for a favored soul to enter divine spellcasting prestige classes, which for the most part are not high-power and are often flavorful and appropriate for a favored soul.
1 really? yes, really. Favored souls have no idea what they’re doing.
Ardent – Complete Psionics
Just about the only good thing to come out of Complete Psionics, the ardent is the psionic take on the cleric: a philosopher more than a priest. Still, psionic mantles are comparable to cleric domains, and the ardent can fill a rather similar role to the cleric.
The better design of psionics makes the ardent, while still very powerful, quite a lot more balanced than the cleric. Fairly comparable to the favored soul in that regard. I’d say the ardent is a little better: more competent in general, but fewer broken tricks. (Broken tricks still definitely exist for the ardent, though.)
Shugenja – Complete Divine
I’ll be honest; I’m kind of guessing about this class’s position here. It might be more powerful than I’m giving it credit for. Shugenja are more-or-less clerics, with an elemental bent. Their spell list isn’t great, but it’s not awful and they get 9th-level spellcasting.
Crusader – Tome of Battle
Handles HP-healing even better than the cleric does (but has zero ability to handle the removal of debuffs, curses, ability damage, and the like until 17th level), and is otherwise a very solid, competent meleer. Basically, if you imagine a spectrum from cleric to paladin, crusaders would land in the middle. Tough as nails and a solid battlefield commander.
One of my personal favorite classes, and my number one recommendation to new players.
Bard – Core, Unearthed Arcana
There’s a divine variant in Unearthed Arcana, but you don’t really even need it. Bards have solid buffs, access to enough healing to help, and can easily take on the role of the cleric as demagogue and evangelist.
A level of sacred exorcist can get a bard (even an arcane bard) the ability to turn undead. Bards are also a natural choice for grabbing that single level of cleric, and having a bunch of wands.
Dread Necromancer – Heroes of Horror
A solid replacement for an evil cleric focusing on minion mastery, the dread necromancer is about as well-suited to leading an undead army as anyone can be. Getting desecrate on the dread necromancer spell list takes some finagling, but if you manage that and get animate dread warrior from Unapproachable East through Advanced Learning, you will literally be the best undead-army leader out there. Even if you don’t, you’ll be quite good at it.
Dread necromancers do cast arcane spells, rather than divine. Houseruling a divine variant isn’t hard, though, and even failing that, learning dread necromancy could just be your interpretation of your evil god’s plan.
Divine Crusader – Complete Divine
A prestige class from Complete Divine, which does mean you’ll need to do something else for five levels before taking it. You get spells up to 9th level, but only those spells from a single cleric domain. Very interesting option; can be fairly powerful but not absurdly powerful.
Paladin – Core
Clerics and paladins end up being pretty similar; clerics actually end up being better at the things the paladin is supposedly better at (martial combat), while the paladin has massively weaker spellcasting. This is a big step down in power, but really quite similar fluff; bizarre that they were in the same book.
Paladins of other alignments exist, in Unearthed Arcana and Dragon. It’s not hard to make them up, either.
The Battle Blessing feat from Complete Champion and the Mystic Fire Knight variant from Champions of Valor, combined with the additions to the paladin spell list from Spell Compendium, combine to make the paladin a half-decent combatant. The Serenity feat from Dragon vol. 306 can also move all paladin class features over to Wisdom, which seems more like a cleric to me (also, mitigates some of the multiple ability dependency). Paladins still struggle in many campaigns, however.
Healer – Player’s Handbook II
By a huge margin, the weakest class in the game to get 9th-level spells. Healers aren’t even all that good at healing, and completely useless at just about everything else. Still, it’s a divine spellcaster, who can heal those debuffs like few other non-clerics can, and if you’re playing a low-enough power game, it could be a good choice. Most likely still a boring choice, but oh well.
The high notes of the druid class include:
Polymorphing. Polymorphing into whatever and getting its stats is almost-always a bad idea, balance-wise, but there are some options for emulating it (or stapling it onto a class so weak otherwise that it works out).
Minions. Between the animal companion and summoning spells, the druid is probably king here. Minions are very problematic for the game in a number of ways (issues with the action economy, issues with consuming real time, etc.), so this is an aspect of the druid that’s probably going to get lost.
Battlefield control. The druid spell list is second only to the sor/wiz spell list in battlefield control, and it is primarily those battlefield control abilities that make the druid as formidable as he is. But many other classes dabble in it in ways that might be useful.
Druid with Shapeshifting variant – Playerr’s Handbook II
This variant replaces both the animal companion and wild shape with “shapeshifting,” an at-will ability that gives minor stat bonuses instead of stealing most of the stats and abilities wholesale off of various animals. Far better balanced.
Note that the druid’s spellcasting is unaffected; this means the druid is still one of the most powerful classes in the game. But shapeshifting explicitly does not work with Natural Spell, and shapeshifting is far weaker than wild shape (plus you lose the animal companion), so this is a fairly large step back in power.
Spirit Shaman – Complete Divine
Is to the druid what the favored soul is to the cleric. Uses the druid spell list, and has an almost-unique form of “prepared spontaneous” spellcasting (the erudite psion from Complete Psionics is the only other class that’s comparable). As with the favored soul, keeping the list (and going to 9th-level spells) means this is still phenomenally powerful – just significantly less so than the druid himself.
Loses all of the druid’s animal companion and wild shape features in favor of mostly-fluff “spirit” features. The spirit companion isn’t even as good as a familiar, and the anti-spirit abilities are not particularly potent.
Totemist – Magic of Incarnum
This is for your wild shaping desires. The totemist can shape “soulmelds” over himself, effectively granting him individual body parts of various magical beasts (such as the four arms of the girallon, the wings of a pegasus, or the tentacles of a kraken). Each of these grants him relevant abilities for the body part, but since it’s not a complete translation, the totemist keeps his own stats, which is a major improvement over the druid.
Warning: while the incarnum system is quite good, and not actually that complicated, the explanation of the system in Magic of Incarnum is ridiculously poor, over-complicating everything and putting important information all over the place so it’s almost impossible to find. Strongly recommend reading Sinfire Titan’s excellent Guide to Incarnum for a superior explanation of how it works.
Wild Shaping Monk or Ranger – Dragon vol. 324, Unearthed Arcana
The full, complete (overpowered) Wild Shape features of the druid, but with none of the other benefits of being a druid. Wild shape is powerful enough to compensate for these generally-weak classes, to make fairly competent warriors.
If it’s still too much, both get “Wild Shape (as druid)” – if you let them replace it, as the druid can, with the shapeshifting variant from Player’s Handbook II, this will significantly reduce the ability to abuse it. (Just ignore the druid’s need to also give up the animal companion for this variant, at least in the case of the monk. The variant is worse than wild shape anyway.)
Ranger – Core
Even without wild shape, the ranger is paladin to the druid’s cleric. Once again, progresses at various features half as fast, and in exchange is supposed to get better martial prowess.... except the druid still ended up better at that, thanks to wild shape.
The Mystic Ranger variant from Dragon vol. 336 can dramatically improve ranger spellcasting, at least until 11th level. As already discussed, the ranger can also get wild shape, and does come with a (weak) animal companion.
This gets you, effectively, a slightly-weaker animal companion. It’s a decent enough feat to tack on to really just about anyone, and can really add to that character’s druidic flavor if desired.
The high notes of the wizard class include:
Everything. Seriously, the sor/wiz spell list has just about everything on it, and a wizard who chooses to focus on any thing will find his spell list ready, willing, and able to support that. For obvious reasons, none of our replacements should have quite that versatility, but it is a common theme among arcanists.
Battlefield control. While the wizard does have everything, this is perhaps what he is best known for. The wizard has fantastic access to spells that just make large sections of the battlefield unavailable to enemies. Which really sucks for those enemies who were already in them. Easier to find lower-power arcanists with solid battlefield control, though.
Debuffs. Second to absolutely-no-one. The “save-or-suck” is a wizard mainstay. Common enough tactic, though, that plenty of other classes have it in more moderate amounts.
Damage. Blasting is a sub-par choice for a wizard, but that should not be taken to mean that the wizard is actually bad at it. There are various reasons why the sorcerer is arguably better for it, though. Lots of options for “wizard-like” blasting at lower power levels.
Sha’ir – Dragon Compendium
An utterly bizarre class, which casts both arcane and divine spells by having a genie go retrieve the spell from an elemental plane (somehow). They’re kind of awkward since they cannot prepare spells for the whole day, but rather only for a limited time before sending their genie off again for a new spell.
It’s weird and awkward, but it is fairly flexible, and they do have access to the entire sor/wiz list plus the divine spells off of several domains, and they progress spellcasting at the same rate as wizards (none of that level-behind nonsense), which is pretty cool for a Charisma-based class.
Wu Jen – Complete Arcane
Literally a wizard with a different spell list. It’s not nearly as good as the sor/wiz spell list, but it’s still plenty good. And the wizard spellcasting mechanic is still very much to their benefit.
Also gains more class features than the wizard does. They’re mostly minor though.
Sorcerer – Core
After favored soul and spirit shaman, you should have seen this coming a mile away.
The sorcerer, however, is much more powerful than those classes. Sorcerers get literally everything that wizards get, which could not be said of the other two with respect to cleric or druid. They just have the limitations of spontaneous spellcasting to deal with. Plus, they do get a few cherries on top as consolation prizes, some of which can be potent enough to make the sorcerer better than a wizard for certain specialties.
Psion – Expanded Psionics Handbook
Effectively the psionic wizard. Because psionics are generally better designed than spellcasting, the psion is too. The fact that psions also function more like spontaneous spellcasters also helps.
The erudite variant from Complete Psionics can make the psion more wizard-like, but the wording on the variant is weak (much like nearly everything else in that book), and certain interpretations can actually make the erudite psion dramatically more powerful than even the wizard.
Beguiler – Player’s Handbook II
A replacement for an enchanter or illusionist, rather than a wizard wholesale. Gets a number of excellent spells from those schools, but limited ability to expand on that list, keeping them in check. Also gets some neat sneaky abilities and far more skills, which is nice.
Dread Necromancer – Heroes of Horror
A replacement for a necromancer, much as beguiler was for an enchanter or illusionist. The minion-mastery is already mentioned as a way to replace an evil cleric, but even ignoring that (which I tend to recommend, minion-mastery tends to be a huge drain on the DM and players’ time), the dread necromancer gets some really solid curse and fear based debuffs. Far more wizardly than animating an army (wizard necromancers tend to do better with a few select specialty undead minions, and then focusing on curses).
Bard – Core
Bards are solid spellcasters; don’t let anyone tell you differently. They do tend to favor illusion and enchantment, but not as strongly as beguilers do. Solid Knowledge skills and the Bardic Knowledge feature also give them a greater emphasis on Intelligence and smarts than most of the above.
Factotum – Dungeonscape
Factota do a little bit of everything, and that includes arcane magic. They also add their Intelligence bonus to just about everything you can think of, making them quite possibly the only class in the game more invested in their Intelligence than the wizard is. A very fun, dynamic class, literally designed around the concept of “Indiana Jones, as he would be in a world of high magic.” Highly recommended.
Shadowcaster – Tome of Magic
Shadowcasters cast mysteries, rather than spells, but are otherwise very similar to a sorcerer or wizard. Mysteries are painfully limited, both in what they can do and how often they can be used, but there are enough decent ones to make something of a shadowcaster.
Ari Marmell, author of the Shadow Magic chapter of Tome of Magic, posted some unofficial errata to the shadowcaster, making the class less painful to play, particularly at low levels (when you’d literally get one spell per day, and then be reduced to plinking things with a crossbow). Still very low-power.
Warmage – Complete Arcane
Probably the second-weakest class to gain 9th-level spells, the Warmage Edge feature is a trap, the warmage spell list leaves a lot to be desired (even within the realm of blasting!), and their other class features are none too exciting. Still, they have a lot of the iconic blasting spells, which makes them look a lot like the way many imagine wizards to look. Definitely a low-power choice.
Warlock – Complete Arcane
Warlocks have access to a lot of very wizard-looking effects – flight, invisibility, teleportation, blasting, curses, zones of damage – but have to pick a very small number of them and stick with them. They do get to use them at will, but most of them only benefit somewhat from that.
Still, for a low-power wizard, warlock is one of the best choices out there. They have access to enough variety to make yourself a conjurer or illusionist or enchanter or necromancer or evoker (not so much on the abjuration, divination, or transmutation, though they do get some of each, including some very nice dispel magic variants), which is excellent.
Spellthief – Complete Adventurer
Spellthieves, as their name suggest, have minimal personal power, and have to steal it from others. This tends to be a massive drawback, though there are some neat tricks you can do with it. Anyway, they have access to the sor/wiz list, albeit only up to 4th level and only from the schools of abjuration, divination, enchantment, illusion, and transmutation. Dragon vol. 353 has a Trickster variant that can bump that up to 6th level (progressing as bard), and also adds all bard spells to the list, though it does cost you most of your “roguish” abilities. Godsblood Spelltheft can also give the spellthief some much-needed reliability.
Truenamer – Tome of Magic
This class doesn’t actually work right, and appears to have never seen any playtesting. Heavy optimization can make it functional, but even then it’s fairly mediocre.
But man, is it cool. A very solid take on what wizardry could be. A damn shame how it turned out.