I wanted a bike that was a reliable commuter/rainbike/winter trainer. The setup that fit that bill perfectly was a fixed gear road bike with fenders. I bought an '89 Trek 660 off eBay for a song, bought a good fixed wheel set, set up the fit to approximate my race bike, and put full fenders and lights on it. A nice low gear ratio (42 x 16 = 69 gear inches) and beefy commute tires meant that I really had to spin it up to get over 20 mph.

I rode it all winter and when the first crit of the season rolled around, I was very pleased--VERY PLEASED--with my fitness. So, to the OP's question, yes, yes I do ride a fixed gear for fitness, pleasure, and to get me to work on time.

And by the way, now that it's spring I've removed the fenders and put on nice light 23mm race tires on it, and it just scorches!