There aren’t a lot of options here, but what we’ve got:
Extra Rage (Complete Warrior)
This is what you should be taking: it grants 2 more uses of rage per day, done and thank you. Seeing as it’s worth a whopping 8 levels of barbarian, most barbarians should take this (and stop taking barbarian levels at about 2nd).
Chaos Rage (Dragon vol. 326)
It’s Practiced Spellcaster, but for barbarians. You count as having 4 more barbarian levels than you actually do, up to a max of your actual character level. That’s worth 1 rage per day, which means you should take Extra Rage and not Chaos Rage.
Chaos Rage does also count as barbarian levels for how strong your rage is, but since rage only improves at 11th, 17th, and 20th, you need a lot more barbarian levels than recommended to ever see that benefit. If using a prestige class that stacks with barbarian levels, maybe, but few do that (most just give more rages per day at their own pace rather than stacking for level). Plus, if it’s a 10-level prestige class that requires that you already have rage, you’re looking at counting as an 11th-level or 12th-level barbarian in total: you already have greater rage, and you’re not getting tireless rage (not that it’s worth a feat anyway). If you find a 5-level prestige class that stacks with barbarian levels, then Chaos Rage looks a lot better, but I don’t think there are any.
The one time Chaos Rage really shines is when you use the berserker strength ACF from Player’s Handbook II, but since berserker strength doesn’t have limited uses per day, it’s entirely irrelevant to this question.
There are more of these than you’d think: obviously there’s barbarian, but several other classes can also get rage through variants and alternative class features.
Barbarian (Player’s Handbook)
1st, 4th, 8th, 12th, 16th, 20th
Obviously, this is the typical source of rage, plus you can get pounce with the lion spirit totem from Complete Champion, and at 2nd, uncanny dodge or Improved Trip with the wolf totem from Unearthed Arcana. So 1 or 2 levels of barbarian is really strong.
On the other hand, another use of rage every 4 levels is really mediocre, and waiting until 11th for greater rage is just a no-go. Everything else about barbarian is mediocre: the DR is tiny, and trap sense is insulting. Barbarian 2nd is probably as far as you ever want to go with the class.
Dragon vol. 349 does offer a devil’s luck ACF that trades the DR for an equal bonus to all saves, as well as a dashing step ACF that trades away trap sense to mitigate the AC penalty for charging—those are both substantial improvements, but still not remotely worth the levels. (The city brawler ACF from the same article, on the other hand, trades away your martial weapon, medium armor, and shield proficiencies for Improved Unarmed Strike and Two-Weapon Fighting—two bonus feats for basically nothing is a steal, and it doesn’t require more barbarian levels to get. You get more bonus feats at higher levels, but again, not worth the levels it takes to get them.)
True barbarian is, RAW anyway, the only way to access most rage variants: battle ecstasy, ferocity, mountain rage, and resilient rage. And it takes some serious squinting to buy another class getting berserker strength—RAW, it says it replaces “rage at 1st,” so any class that gets that should be OK, but the whole description is full of “barbarian” and it’s under a “Barbarian” heading. The only one that’s arguably problematic to give to another class is resilient rage, since it’s on a variant that also trades away the barbarian’s fast movement, but that’s a discussion you’d have to have with your DM.
Whirling frenzy, though, that one is explicitly a variant of rage, not a variation or option for barbarian. That can definitely be chosen by any class that gets rage.
Druidic Avenger (Unearthed Arcana)
1st, 6th, 11th, 16th
The druidic avenger variant druid gets rage, but at a slower pace and never gets improvements of that ability. On the other hand, druid is offering a whole lot more in terms of other class features, including, most importantly, wild shape. Having both rage and wild shape at the same time is incredible.
You do lose out on the animal companion, which is a shame, and wild empathy, which isn’t unless you needed it for a requirement or something. Ultimately, the animal companion is superior, because it has its own actions and rage interferes with your spellcasting, but still, this is a strong class.
Even with the interference from rage, spellcasting is still the strongest feature a druidic avenger has. Raging is a free action, so loading up on buff spells before combat, and then raging and wild shaping, is a great strategy. You probably still want Natural Spell, if only so you can scout or snipe from the air with your spells.
Stacking between barbarian and druidic avenger is unclear. They’re probably separate progressions (so a 1st-level barbarian/1st-level druidic avenger gets two daily rages), but it’s not immediately clear that this is the case; Unearthed Arcana doesn’t really address it. See this Q&A for more details.
Druidic avenger is also notably compatible with this variant druid, also from Unearthed Arcana, which trades wild shape for a lot of monk and ranger features—a very good deal if you were never going to take enough levels to get wild shape anyway (an utterly atrocious deal if you were going to get wild shape, of course).
Even more so than a regular barbarian, a druidic avenger needs to take Extra Rage.
Rage Cleric (“The Rage Cleric,” Dragon vol. 333)
1st, 4th, 8th, 12th, 16th, 20th (stacks with barbarian)
Trade both domains and turn undead for rage. Ultimately, this suffers from the same problems as the druidic avenger—raging interferes with spells—and gives up a lot more, and it doesn’t have wild shape to fill in. Buffing and then raging still remains a totally viable strategy (particularly with Divine Metamagic), but I’d rather keep the domains and turn undead.
Raging Monk (“Variant Fist,” Dragon vol. 310)
1st, 4th, 8th, 12th, 16th, 20th (stacks with barbarian)
Trade flurry of blows, still mind, and quivering palm for rage as a barbarian. Explicitly stacks with barbarian levels (and so also stacks with everything else that stacks with those).
This is a solid option for getting some rage: monk has a ton of options for bonus feats in the first two levels, and Improved Unarmed Strike shows up in a lot of requirements, too. At 2nd, evasion is nice; invisible fist (Exemplars of Evil) is better.
(Obviously, cleric or druid is just better, even though they gave up more and rage interferes with their spellcasting, because spellcasting is just that good. This just might feel better since it’s a better trade.)
Beyond 2nd, monk mostly stops being a viable class. Dragon vol. 324 changes that with wild monk, which gets wild shape, but it isn’t compatible with raging monk since both lose still mind and quivering palm. Still, it may be worth asking your DM if trading away resist nature’s lure and wild shape (tiny), the features wild monk gains at the same levels that a monk gains still mind and quivering palm, would work. Still mind and quivering palm are pretty crap, so I for one would have no objections—wild shape (tiny) is way better than both combined.
Racial Paragon Classes
Racial paragon classes are weird, they’re kinda like mini-prestige classes that can actually be taken right from 1st since the only thing they require is a race. They’re mostly not terribly good, but one is relevant:
Half-orc Paragon (Unearthed Arcana) (2nd)
Half-orc paragon gets a daily usage of rage at 2nd level. Notable mostly for its lack of alignment requirements on something that doesn’t require Dragon magazine, but the druidic avenger’s “any neutral” is pretty flexible.
Since half-orc is a terrible race, this probably isn’t too great an idea. The first level is pretty much dead, too.
Unsurprisingly, lots of options here. Frenzied berserker is the best of them, really, though frenzy isn’t quite rage even if it counts for many purposes. Beyond that, pickings are kinda slim...
Battle Howler of Gruumsh (Dragon vol. 311)
2nd, 5th (min. ECL 7th, 10th)
You get both bardic music and rage. Not terrible, but the requirements are.
Bear Warrior (Complete Warrior)
7th (min. ECL 14th)
Turn into a bear when you rage. Ultimately, this is fairly strong, much stronger than more levels of barbarian, but the class has a lot of dead levels, and when you compare to getting proper wild shape (via druidic avenger, or raging monk if allowed, or just multiclassing wild-shape ranger) it just loses a lot of appeal.
For the sake of getting uses of rage, abysmal.
Black Blood Cultist (Champions of Ruin)
varies (stacks with barbarian)
This is one of the most absurd prestige classes in the game, really, because the 8th-level savage grapple feature deals the damage of all your natural weapons simultaneously on each and every successful grapple check. Considering all the myriad ways to stack enormous numbers of natural weapons, this is patently ridiculous.
Nothing else about the class is notable, though.
Chameleon (Races of Destiny)
3rd, 6th, 9th (one of several options for mimic class ability) (min. ECL 8th, 11th, 14th)
At 3rd, 6th, and 9th level, get a daily use of mimic class ability, which includes rage as an option. Chameleon is a cool class, but it’s not really a great fit for a barbarian usually.
Champion of Gwynharwyf (Book of Exalted Deeds)
varies (stacks with barbarian)
Champion of Gwynharwyf stacks with barbarian levels to determine how and how often you can rage, so that’s something. With 10 levels, you’ll actually get greater rage. More importantly, at 2nd level you get the ability to cast champion spells while raging, and at 4th you get a rather-potent Intimidate aura whenever you rage. And this is on top of a class that is already very defensively powerful, regardless of rage: there’s DR, resistances, immunities, and divine grace in there.
Unfortunately, it requires that you take two feats and absolutely set them on fire, and the BAB +6 requirement means a later start (especially if taking some non-full-BAB class levels). And the spellcasting you get and can cast during a rage is rather mediocre.
Eye of Gruumsh (Complete Warrior)
varies (stacks with barbarian)
Really doesn’t have a whole lot going for it, but I guess it’s better than base barbarian. Though the cost of two awful feats (Exotic Weapon Proficiency and Weapon Focus in orc double axes) probably negates any advantage it had over barbarian.
Frenzied Berserker (Complete Warrior)
1st, 3rd, 5th, 7th, 9th (frenzy) (min. ECL 7th, 9th, 11th, 13th, 15th)
Note that frenzied berserker is a very divisive class. There are ways for a party to protect themselves against the risks of associating with a frenzied berserker, but a lot of groups don’t want the bother. Always ask before playing one—ask everyone, not just the DM, because it’s your fellow players who are going to have to deal with it the most. (While you’re at it, ask about the Righteous Wrath feat, as discussed at the end of this answer—even if your group is OK with the problems, if you can fix those with just one feat and you don’t, that’s pretty rude.)
That’s a ton of frenzy, which is like super-powered rage—except it forces you to keep attacking even if all the enemies are down. It’s got other downsides, too. As noted, there’s ways to handle frenzy, but it has to be handled.
On top of the frenzy, other frenzied berserker class features are strong too. Frenzied berserker is by-far the best barbarian-focused prestige class.
Note that frenzied berserker does not grant more uses of rage, itself. Frenzy counts as rage for a lot of purposes but you’ll have to use one of your daily rage uses to actually get the benefits of rage, and frenzied berserker won’t help you with those.
Hida Defender (Oriental Adventures)
2nd, 4th, 6th, 8th, 10th (min. ECL 7th, 9th, 11th, 13th, 15th)
Gets a use of rage on every even level, which is quite a pace compared to the barbarian. Gets DR on most of the odd levels, too, for up to DR 4/–: far too little to really make much difference, but again, way faster than the barbarian gets it. Requirements aren’t too onerous, either (heavy armor proficiency, Power Attack and Weapon Focus). Not really a great choice but it exists.
Kinslayer (Drow of the Underdark)
1st, 5th, 9th (min. ECL 2nd, 6th, 10th if a lesser drow with flaws)
Little of note, but there is a use of rage at 1st, 5th, and 9th. Mettle (not tied to rage) at 1st isn’t bad either. But not worth four terrible feats, even if you can do it at really low level with the right variants.
Rage Mage (Complete Warrior)
3rd, 8th (min. ECL 8th, 13th) (also spell rage: 1st/6th, 5th/10th, 10th/15th)
Garbage class that’s terrible at what it does. You get extremely minimal ability to cast spells in a rage, but it’s not enough to be worth the levels or the requirements.
Runescarred Berserker (Unapproachable East)
2nd, 5th, 9th (min. ECL 9th, 12th, 16th)
You can fight in your own antimagic field, and then use heal on yourself afterwards. That’s strong, at least so long as your game stays grounded or you find some nonmagical source of flight (e.g. dragonborn, raptoran, feathered wings fiendish graft). It is, on the other hand, a little one-note, though you can always abuse polymorph for more versatility.
Note that antimagic field, heal, and polymorph are all 5th-level runescars, only available at 9th. Before that, there’s haste, freedom of movement, and death ward, as 3rd-level spells, starting from 5th, so that’s pretty good, but earlier than that there’s not a whole lot.
Singh Rager (Oriental Adventures)
2nd-or-3rd: 3 uses, 6th, 10th (min. ECL 9th or 10th, 13th, 17th) (see below)
So singh rager gets a “lion’s fury” class feature which is literally a copy-paste of rage, including saying it grants the ability to “enter a rage.” So it’s a tiny bit unclear if that means it counts as rage, but it probably does. And it gets three uses at once, which is a pretty big deal. Another problem: there’s an error here, and the feature says both 2nd level and 3rd level:
Lion’s Fury (Ex): At 2nd level, [...] A singh rager can enter a rage three times per day at 3rd level,
Note that prior to the line about getting three uses at 3rd level, there is nothing in the feature about how often it can be used. One could even argue that, strict RAW, you get infinite uses at 2nd level, since at that level no rule applies that limits how much it can be used. For what it’s worth, the table lists “Lion’s fury 3/day” at 2nd.
You definitely get another use at 6th and again at 10th, not that the class has much of anything else worth hanging around that long for. Requirements aren’t too terrible, though the Lawful requirement could something of an issue.
Totem Rager (Magic of Incarnum)
2nd, 8th (min. ECL 8th, 15th)
Probably the best option for dedicated “rage and” classes, meldshaping plays nice with rage and the the progression here is fairly strong (meldshaping on all levels but 1st), though the chakra progression is mediocre. More mediocre is the rage progression, which is even worse than barbarian’s.
Sadly, even if it might be the “best” dual-progression class for rage, it still probably isn’t worth using. Your rage progression is better handled by just taking Extra Rage after barbarian 1st, and spending the rest of your levels in totemist: you’ll have nearly as good rage, and much better meldshaping. Barbarian 1st is a great dip for a totemist, but none of the barbarian/totemist options in Magic of Incarnum are any good.
Warrior Skald (Races of Faerûn)
10th (words of fury, applies to whole party)
Only one use of rage, but it’s rage for the whole party (who want it). In theory, that means you could get a warrior skald cohort to use it on you, making Leadership an option for a use of rage as a feat.
Otherwise, it’s a more combat-oriented, spell-less, bard. Which means it’s not great, but you do get all the bard’s bardic music effects, plus some unique ones, so it’s something. Has terrible requirements, but they happen to be the same terrible requirements as battle howler of Gruumsh, so that’s something too.