Above all else, I want most classes with an animal companion to give me the ability to "opt out" of it. Really though, I don't see why any class couldn't have an animal companion, though I'm sure some would emphasize it more than others.
The talk was that it wasn't classes that got the companions... but rather the themes. So the way to 'opt out' of a companion would be to just not take a theme that included one. If your wizard doesn't want a familiar, there will probably be numerous themes that don't include one that you could take instead.