Fixed Gear
or the joys of 1880's technology
Trackbike 
Less is more, this is the bike I tend to ride most. A fixed-gear bike has no gearchange which makes cycling wonderfully uncomplicated. You never realise how hard those decisions to shift gear are untill the option is removed. And the frontbrake (a rearbrake is unnecessary) can be left alone most of the time as well. In short, a fixed gear bike is ideally suited to ride away the stresses of everyday life, not in the least because of the absence of annoying rattles. 
And the smooth transmission (44-17) is supposed to work wonders for your pedalling technique. On the minus side you have to take a bit of care in corners as the inside pedal will allways come round to its lowest position from time to time, and a balanced position is compromised with your legs going up and down. Stopping pedalling will also give you a nasty surprise! (I use SPD's)
freehub drawing See for more advice on fixed-gear cycling Sheldon Browns goldmine: Harris Cyclery, West Newton, Massachusetts
A problem when building a fixed gear bike is how to find a suitable rearwheel. I couldn't locate a wholesaler or shop with track stuff at first, so I made my own.
You can install a threaded cog (from an old style coaster brake) on a freewheel type rearhub (screw it tight, use Loctite and a LH bracket lockring), but to get some sort of chainline you have respace the axle with loads of washers and reverse the wheeldish which certainly looks funny! Proper trackhubs have the flanges much further apart for a symmetric wheel. On the subject of cogs, some people use Shimano UG locking cogs, which are suitable for use with narrow chains, but the threading is not quite BSC, so reliability or the hub may suffer. A proper trackcog is probably best.
An other approach which does away with threaded cogs is to convert a Shimano freehub. This can be done with exotic CNC machined parts (Surly?), or by welding up the genuine article.

Procede as follows:

  • Start with the removal of the axle and the dustshield of the outer freehub bearing
  • The bearingcup becomes now visible, and can be loosend using either a drift (lh thread, the notch is visible in the picture above) or the proper Shimano tool
  • Now remove the freewheelbody from the hub with a 10 mm Allenkey
  • Remove the bearing cup (a lot of small bearings will drop out, but you won't need them again) and degrease
  • Replace the bearings with rings turned on a lathe or made from 3mm steel wire wrapped round a suitable bar to fill the space previously taken by the bearings, and refit the bearingcup
  • TIG-weld the reverse side of the freewheelbody

  •  
Rebuild the hub, and fit a cog (a Shimano BMX freehub cog with big teeth would be nice) together with a stack of spacers salvaged from junked cassettes. If your horizontal dropouts are long enough you could even fit two cogs for a change in gearing.
respaced hub for fixed gearproper trackhub
a standard hub (left) vs a proper trackhub (right)