Someone who has ridden singlespeed mountain bikes for many many many years and singlespeed road bikes also, I have just switched an old bike to a fixed gear for the first time as my around towner. And here is what I've found in two days.

Fixie:

Pros:
Easier to keep speed
Very little maintenance
Fun

Cons:
Hills are harder to slow down on
Sometimes you just want to coast

Now I will explain on the keeping speed, the bike is helping you keep that speed from the momentum being used that is pushing the tire and the pedals. All I have to do is apply force at certain points to keep the speed I want I do not have to push/pull much. I have taken my feet off the pedals to just coast and that does help. The first day I had no brake, but I know my city well and am not in much danger, I since put a brake up front.