Other than (limited) wish, are there any feats/prestige classes/etc. that could (directly or indirectly) give a wizard access to things like cure X wounds, remove disease, raise dead, greater restoration, or regeneration (especially since those last two can't be wished)?
The main goal is a character who can heal without divine magic, so something like a bard (who uses arcane magic but still gets to cure wounds) would also work, if it were a full-caster with spells up to 9th level.
With all of these, bear in mind that all of the spells mentioned in the question are very weak. Heal is the one really strong healing spell (well, and mass heal), the restoration spells are necessary but not stellar, and the cure spells are just bad. Investing resources for access to them is probably a poor idea, particularly since all of these (heal, again, excepted) are easily replaced by magic items.
The sublime chord from Complete Arcane is a prestige class that has 4th-9th level spells from the bard and/or sor/wiz spell lists. As the bard list includes various cure spells, it meets your requirements. Since the bard list stops at 6th-level, however, and the sor/wiz list does not include any healing spells, this may not be what you had in mind.
The wyrm wizard prestige class from Dragon Magic allows you to learn “one spell from any class's spell list (including divine spells)” at each even level. It does note, however, that aside from adding the spell to your arcane spell list, “all other aspects of the spell remain unchanged,” which may or may not mean you cast it as a divine spell if it was before; it’s unclear.
Wyrm wizard also misses out on spellcasting progression at 2nd, 4th, and 6th, making learning spells in this fashion very expensive. Still, just enough, for a wizard anyway, to reach 9th-level spells.
The rainbow servant prestige class requires 3rd-level arcane spells, and at 10th level, grants “cleric spell access,” allowing the arcane spellcaster to learn and cast cleric spells. However, it also explicitly notes that “Such spells are cast as divine spells if they don’t appear on the sorcerer/wizard or bard spell lists,” which means that you can get the cure spells that the bard has as arcane spells, but the rest are divine for you.
There is another problem, too: a discrepancy in the class description’s text and table.
Spells per Day/Spells Known: When a new rainbow servant level is gained, the character gains new spells per day as if she had also gained a level in whatever spellcasting class in which she could cast 3rd-level arcane spells before she added the prestige class.
vs.
Class Level … Spells per Day 1st … — 2nd … +1 level of arcane spellcasting class 3rd … +1 level of arcane spellcasting class 4th … — 5th … +1 level of arcane spellcasting class 6th … +1 level of arcane spellcasting class 7th … — 8th … +1 level of arcane spellcasting class 9th … +1 level of arcane spellcasting class 10th … —
The actual “Spells per Day/Spells Known” class feature makes no mention of the 1st, 4th, 7th, and 10th levels of the class not advancing spellcasting—it says “when a new rainbow servant level is gained,” no caveats on which levels. The table, of course, indicates four lost spellcasting levels.
The errata rules for this situation are explicit and clear: text trumps table. Officially, RAW, rainbow servant advances spellcasting at every level. This is, of course, very powerful—though honestly it’s far from the most powerful prestige class a wizard could take—but the alternative, making it a 6/10 prestige class, makes a self-nerf to take it, as cleric spell access is not worth four lost spellcasting levels. (Even a mystic theurge—also categorically not worth it—only loses three.) Importantly, losing four spellcasting levels as a wizard means you are no longer going to be able to cast 9th-level spells by 20th.
Each of these requires you be able to cast divine spells, so probably not a real answer to your question, but the Complete Divine geomancer’s spell versatility (1st-level class feature), as well as the Alternate Source Spell (Dragon vol. 325) and the Southern Magician (Races of Faerûn) feats, allow you to cast a divine spell as arcane (or vice versa). That would allow you to take any of the spells you are interested in from a divine class, and cast them as arcane—so long as you can cast them as divine spells first.
Probably not what you want.
Complete Divine details how extra domains work for wizards:
If [the character who got a domain] is a spellcaster who keeps a spellbook as a wizard does, then she must find or purchase a scroll of that spell and pay the usual price to scribe the spell into her spellbook. In cases where the spell is only divine the wizard may scribe a divine scroll into his book. The wizard then may memorize one domain spell of each level each day. [...] Unless the prestige class specifies otherwise, such spells are considered arcane spells when cast by arcane spellcasters.
So if you could choose domains that offer the spells you want—for examples, Healing and/or Renewal—you’d be good. Complicating this process, however, is that no deity offers both domains, so to get both you’d have to find options that allow you to get the domains from “ideals” as clerics can.
The divine oracle, rainbow servant, and sacred exorcist prestige classes from Complete Divine are accessible by wizards, and grant domains, though the domains they grant (Oracle, Good/Air/Law, and Exorcism, respectively) are unhelpful—though of course, rainbow servant’s capstone solves that concern.
Complete Divine does also provide the Arcane Disciple feat, as Emil S. Jørgensen’s answer notes. This is a sub-par solution, however, as Arcane Disciple forces you to use Wisdom for those spells instead of Intelligence or Charisma—the save DC probably won’t matter, but the minimum Wisdom to learn them in the first place might. More importantly, while you could take it twice, in theory, to gain both the Healing and Renewal domains, again no deity offers both.
Outside of Complete Divine, there don’t seem to be any prestige classes granting domains to arcanists.
We could, however, abuse one of the arcane-as-divine options above, to qualify for a prestige class more generally aimed at divine spellcasters. That gives us some options:
each grant any one domain available through your deity. Meanwhile
grants one domain off of a short list that includes Healing.
Problem: Divine disciple also advances only divine spellcasting, and divine agent, while it advances any spellcasting, only does so on even levels. Still, contemplative or singer of concordance could be viable.
Note that all of these prestige classes require worshiping a deity, and in the singer of concordance’s case that must be Io specifically. Again, no deity offers both Healing and Renewal. So this gets us Intelligence-based (or Charisma-based) arcane healing, but still requires a deity’s influence and still prevents us from getting all of it.
Combining the Arcane Disciple feat ( Complete Divine, p. 79) with a Cleric Domain that grants access to Restoration, like the Renewal domain ( Spell Compendium, p. 279), should do it.
You can use the Healing domain for Cure X and Regenerate ( Players Handbook, p. 187 ).
Now your greatest problem is finding a deity that supports both domains.
The Sublime Chord prestige class (Complete arcane, page 60), is pretty much designed explicitly to turn bards into full casters. The classic progression is Bard 10/Sublime Chord 10. This will leave you with 9th level spells by level 19, access to the full bard list, and access to the wizard/sorcerer list for everything about 4th-level spells. It won't give you the higher-level healing spells, unfortunately, but it's a generally solid build.
If you have access to Eberron, are willing to spend feats on it, and are willing to play a halfling of House Jorasco, Mark of Healing gives access to Cure Light Wounds and Lesser Restoration at Least, Cure Serious Wounds and Restoration at Lesser, and Heal at Greater. It's not much access, though, and it's not a terribly efficient build choice overall. It's also not technically arcane - these are spell-like abilities, rather than spells. It is, however, entirely not divine, which looks like it might be what your'e looking for.
It's pretty thin on the ground, though. There are sources of non-Divine healing in D&D 3.5 (Dragon Shaman, one of the Incarnum binds, freaking Truenamers...), but they're all pretty weak/secondary.
