Mage, Necromancer, Beastlord, Shaman and Shadowknight all get true pets. There's considerable debate about who has the strongest pet between Mages, Beastlords and Necromancers. All three are fairly strong and very useful.
Enchanters get a pet but can't control it until they spend some AAs.
Enchanters, Bards, and Druids can charm pets with some limitations. High level Enchanters are very good at this.
Druids and Wizards get something like a pet but not really. Druids get a really gimp bear and wizards can summon a familiar that's little more than a graphic buff.
There may be more but that's all I can think of.