I ride fixed gear bikes for the same reason that I love driving stick shift and riding a motorcycle. It's ALOT of fun. I have much more control, its like third gear(in a car) all the time, more feedback from the bike and the constant pedaling is a great workout. My legs are carved from wood these days and I can eat like a pig and still lose weight.
The bikes are very pretty too. No clutter, what with the derailleurs and shifters and all. Not to say I don't have geared bikes, but my fixed gears are my favourites.
Also, I was getting bored with bikes. Almost giving up on them. When I started riding fixed a few years ago, I fell in love with cycling all over again. It also helps you become a much stronger rider with a much smoother pedal stroke. It helped me smoke my riding buddies on climbs in the woods on MTN bikes.
Anyhow, that preceding convoluted mess is why a fixed gear bike is a must for me.