The primary limitations are 1) Skill, 2) Time, and 3) Cash
Animals need feeding - "Feed" is listed in the SRD under Equipment/Goods And Services at 5 cp/day, 10 lbs/day for Horses, Donkeys, Mules, et cetera; for Carnivores, chunks of meat are listed at 3 sp per 1/2 lb (if you have a lot of carnivores (or a few big carnivores), you are probably better off buying mules or donkies and slaughtering them yourself).
Pretending any Large herbavore eats the same as a horse, you can scale fairly easily - a size class (usually approximates as x2 in each dimension) works out to a * or / 8 (mass) for each size class up or down (probably use 4 for food intake, as it doesn't scale perfectly with mass) - so a Huge herbavore would need 40 lbs of feed a day (2 sp), a medium: 2.5 lbs (1.25 cp).
Carnivores are harder to judge, of course, as game-mechanics don't include a baseline for comparison - if, however, we assume that a Large Carnivore needs the same mass of meat as a Large Herbavore needs feed, then your medium Wolf needs 2.5 lbs of meat a day (1.5 gp), while your Large Dire Tiger needs 10 lbs of meat a day (6 gp); as I mentioned - you will probably be better off buying a Donkey every few days (8 gp each) to feed your Dire Tiger.
Also, there is a problem with raising animals - with a DC of 15 + Animal's HD, a character (cha 16, Animal Affinity, max ranks in Handle Animal, for this example) can't reliably (take 10 succeeds) rear wild animals with more than 3 HD than the character has levels (8 hd for level 5, 13HD for level 10, and so on). Moreover, exotic animal cubs are very difficult or very expensive to get - if you can take a Dire Tiger's cubs away in relative safety, those grown-up Dire Tigers won't be too terribly much help.... even if you can raise them safely. For the same reason, exotic animal cubs would be expensive - they are hard to get, and difficult to train. Call it 50 gp * CR(of the final animal) ^ 2, for the cubs; that would be 200 for a heavy warhorse "cub", 800 gp for a tiger cub, 450 gp for a Huge Viper "cub", 3200 gp for a Dire Tiger cub.
It's extremely unlikely that the grown versions would be available already domesticated, due to the difficulty of raising them - how much does it cost to hire a skilled trainer, especially one who can reliably raise the more difficult creatures, as hired NPC's usually don't have big stat bonuses (usually just the minimum needed to cast the spell with spellcasters) for the time it takes one of the more difficult creatures to grow up (how many years does it take a normal tiger to reach adulthood? Two, three years? Four?)? A max-rank NPC with Animal Affinity and no stat bonus is only going to be able to rear an animal (Level + 3 + 2 (AA) + 10 (for take 10) = Level + 15; DC 15 -> Reliably of the NPC's level) of the NPC's level or less in HD. Let's see.... at 3 sp * level^2 per day, a level-1 trainer costs 365*3 sp = 1095 sp/year. A three-year critter with 10 final HD would thus cost 328,500 sp, or 32,850 gp for rearing alone. Three of the same kind can be done simultaneously (and thus you can divide the cost by 3 for a "professional" exotic animal rearer), but that is still 10,950 gp rearing costs for a 10 HD animal - and that doesn't include the cost of the cub itself, nor the feeding of that cub.
Just in case you want to tone down a Player who wants lots of pets, or if you need to discuss things with a GM to ensure that you can have a few.