Unless you're talking about more-or-less immobile pets (like a small fish or turtle tank), you'll have a variety of problems (some of which were already mentioned):
- waste elimination
- noise (all dogs bark - unless you've clipped the vocal chords)
- keeping it "contained" (are you really going to crate your cat next to your desk all day?)
- safety (from having to evacuate the iguana in a fire drill to making sure no-one trips over the cage or animal)
- regulations (eg OSHA requirements)
If you deal will all of those (and, I'm sure, others I've missed), then and only then can you think about bringing it up with your boss.
As others said, make sure you get buy-in from your coworkers! For example, I despise cats - I'm allergic and I don't like them. If you wanted to bring your cat into an office I worked in, you'd get an adamant "no" from me :)
It might be a good idea to get buy-in from the staff and then propose an office "pet" - like a fish tank - that everyone can enjoy, and someone (or ones) take care of some type of schedule (like a doctor or dentist office may).
For people like me who frequent work from home
If you're spouse/roommate/SO is OK with it - then bingo: you have a pet in the "workplace"