Hamsters - not because I hate rodents (I adore
rats and guinea pigs!) but my experience working in a pet shop has taught me that hamsters are jerks, and often finicky as all hell. Of course they can be hand-tamed, but it's just so much easier to do so with a rat. Rats are way smarter, anyway, so they're often more interesting to watch.
And no fish of any kind. You can't handle them and their care is very precise and involved, especially for something you really can only look at. The same goes for anoles, frogs, chameleons, or water turtles (these guys can
be handled, but they tend to react poorly to it).
Actually, any animal that can't be handled or is very difficult to acclimate to handling is off my list of acceptable pets.