depends on your class and your level (and what expansion(s) you have). starting with Echoes of Faydwer, Norrath saw the return of the gods. started with only a few, but as time has progressed, more have come back. if you choose to follow one of the gods, you will be given a quest series of 5 quests. the third (usually, though I know of one for sure that isn't on the third quest) rewards you with a pet that will give you some stat(s) a boost.
Other than the diety pets, the only other classes that benefit from having pets are the pet classes (conj and necro, specifically, though illusionist also, if you solo). most of the other "pets" that players have following them around are fluff. just for show. nothing important.
HTH.