I love riding my fixie, if you can't tell from my user name . I came to it as a mountain biker, and feel that the effort of riding hilly terrain helped prepare me for anerobic efforts. I ride it on single track, and it's a completely different experience from riding the gearie and makes old trails new again.
It also engrained good cadence and smooth pedal stoke into my muscle memory so that I felt at complete ease when I started riding a road bike with roadies.

I can get a little spiritual talking about fixed gear riding, so I'll stop before I get to waxing poetic about the Zen aspect .