Anthropomorphic animals are a staple of fantasy fiction. Fortunately, they are easy enough to hack into any edition. Anthropomorphic animals are simply other races reskinned. This gives you an existing race and all its racial feats, along with any other racial rules might be helpful to you.
Humans work well for monkeys and other well rounded animals, such as badgers.
Dwarf traits are very useful for solid, well-built animals. There not much difference between a dwarf and a hog, for example. Rams also work well with dwarves.
Half-orcs are best used for solid animals that have known mean streaks, such as boars, rhinos, and hippos. (Don’t laugh at hippos. They’re more deadly than lions.)
Half-giants and other particularly large races work well with any larger animals, such as moose, elephant, or bison.
Elves go well with very agile and graceful animals, such as deer, snakes, and birds.
Halflings associate well with clever animals, such as fox or wildcat.
You might want some bonus skills to come with your animal choice. Especially in 3.X, it’s hard to go wrong by adding appropriate skills. You could also add a free Skill Focus if a class already has an appropriate feat. So a fox might give a fighter the Sneak skill, but would give the rogue a Skill Focus feat since that class already has Sneak.
That was easy, wasn’t it? The combinations are pretty simple once you get used to the cheat.