We have had just about every pet imaginable!
Everyone knows about cats and dogs, but we also had:
Hamsters- Not all that lovable, escape artists, not really trainable, and sometimes even the most friendly ones bite.
Rats-more friendly and trainable than hamsters, but a lot of people have hang-ups about getting a rat.
Ferrets-VERY lovable and friendly, smart as heck, trainable, you could litter-train and let run free, get along with other pets if trained right... but they stink. Even if they are unscented, bathed regularly, de-scent stuff added to water, and cage cleaned... there will always be that ferrety smell.
Chinchilla- Kinda like a giant ultra-soft hamster without the escape-artistry... needs a dust bath every day, which is really fun and cute to watch... we used vanilla scented dust, which added to the appeal. The main problem with Chuck (hee hee. chuck the chinchilla) was that he pooped A LOT! every time we held him we wound up with a handful of little black pellets. Put him in an exercise ball, it gets in the air cracks.
Fish- fun to look at, but that's about it.
Birds- we had canaries and parrots... parrots are high maintenance and get pretty annoying sometimes... my canary flew away. :'(
Hedgehog-One of my favorite pets because it was soo unique... One was super-friendly and the other not so much. Had to wear gloves to handle her. They also kinda smell bad.
Rabbits-Fairly lovable... I didn't really work on training mine so much, but apparently my SIL had hers box-trained! :)
Turtle- We had a little water turtle and a small tortoise... the turtle was not much fun, but my brother really liked it. (it was his...) The tortoise was better, but still kinda boring. Not much you can do with something so slow.
Good luck! My vote is cat by the way.