You won't have a persistent pet that is there when you log back on, but you can charm pets (Mentalist (light) or Sorcerer) and have someone buff them up to make them insanely tough and drag them around with you whever you go unless you have to load a zone.
You can summon a pet or several pets depending on some classes (Enchanter, Cabalist, Spiritmaster, Bonedancer, Theurgist (kinda), Animist (non mobile turrets), and probably another few I might be missing)
There is no pet that goes into your inventory except the new horses that don't fight for you.