I am by no means an expert. Check out Sheldon Brown's (R.I.P.) website for super detailed information. Here's my reasons:

1. It's just as mechanically efficient as a single speed, if not better.
2. Better control of the bike with the ability to slow down by resisting the pedal motion
3. Creates a smoother pedal cadence
4. A fixed gear drive train "feels" better to me
5. Increased fitness from "always pedaling" and it develops leg muscles not used on a single speed (through resisting pedal motion)
6. Technically, a fixed gear is a simpler machine since it does not require a freewheel
Keep in mind that I live in Philadelphia, which is a pretty flat city.