What I am looking for is a complete list of every class and prestige class in any of the first party WotC-published D&D 3.0 or 3.5 rulebooks that stacks with other classes in determining the bonuses of an Animal Companion either by increasing effective druid level or otherwise.
I can think of druid, ranger, beastmaster, halfling outrider, wild plains outrider, arcane hierophant, and lion of talisid off the top of my head. I don't think there are a whole lot more than that but I want to be aware of all of them. If there are resources that provide this info, could you point me toward those resources?
Best Answer
Posted originally in 2008 on the Wizards of the Coast boards here and updated in May 2010 on the Minmax Boards here, Surreal's List of Stuff, in addition to providing a great deal more, lists classes that improve one's animal companion. I assume--given the amount of research in other areas--that its animal companion information is comprehensive (the absence of the halfling outrider notwithstanding), but it does exclude Dragon and Dungeon magazines.
Below I've confirmed that the prestige classes do, in fact, advance animal companions as the List of Stuff's commentary is either absent or telegraphic.
From the List of Stuff
The prestige class abolisher (LoM 182) at level 1 gains the ability animal companions. It reads, in part,
The prestige class arcane hierophant (RW 108) at level 1 gains the ability companion familiar. It reads, in part,
The prestige class animal lord (CAd 22) at level 1 gains the extraordinary ability animal bond. It reads, in part,
The prestige class beastmaster (CAd 26) at level 1 gains the extraordinary ability animal companion. It reads, in part,
The prestige class gatekeeper mystagogue (PE 87) at level 1 gains the ability animal companion. It reads, in part,
The prestige class lion of Talisid (BE 65) at level 1 gains the extraordinary ability animal companion. It reads
The prestige class peregrine runner (RS 116) at level 1 gains the extraordinary ability peregrine companion. It reads, in part,
The prestige class planar shepherd (FE 105) at level 1 gains the ability animal companion. It reads
The prestige class revenant blade (PE 142) at level 1 gains the ability ranger class features. This reads, in part,
The prestige class Vandalis beastkeeper (Dra 130) at level 1 gains the extraordinary ability improved companion or mount. It reads, in part,
The prestige class wavekeeper (Sto 76) at level 2 gains the extraordinary ability beast of the sea. It reads, in part,
The prestige class wild plains outrider (CAd 92) at level 1 gains the ability animal companion/special mount. It reads, in part,
Not from the List of Stuff
The prestige class halfling outrider (CW 38) at level 1 gains the ability mount. It reads, in part,
The prestige class legacy champion (WoL 19) at every level except 1 and 7 gains the ability class features (seriously, the special ability is named class features so it has a class feature called class features). It reads, in part,
Ten levels of the class should increase by 8 the character's level for his animal companion ability among all but the most conservative DMs but, as always, ask.
I'm happy to update this based on Comments and my research. As the question asks only for prestige classes, just those'll be listed, despite other animal companion resources being awesome (e.g. the feat Devoted Tracker (CAd 108), the alternative class feature urban companion ("Cityscape, Part 1: Urban Class Features" here).