Check this out:
Info on fixed-gears and conversions:
I bought an old used Cannondale for $150 and converted it (thanks to a local bikeshop guy) with about $200 worth of parts and labor. I've never been happier.
If you wish to make your own "from scratch", I highly suggest trying to buy a frame/bike that already has the horizontal rear dropouts. My Cannondale did not--thanks to the Sheldon Brown website and some minor filing to deepen my 45-degree dropouts, it thankfully worked out okay. The last bikeshop guy who serviced my bike would have liked to have seen a tiny bit more tension in my chain, it has ridden just fine (up big hills with a lot of tension) for a long time that way and the work to fix it is just too much effort and may screw things up more. FYI.
One thing I did with the bike to both make it have less flat tires and add to the ride exertion was:
1) Heavy-duty Specialized Armadillo tires
2) Mr. Tuffy Tire Liners between the tire and the tube
3) Extra-thick inner tubes
Lots of extra "unsprung" weight, I'm not in any races though...
Knock on wood, no flats yet. I don't expect any either.