I ride a fixed gear bike on the street. No I don't have a handlebar moustache.
I enjoy riding it a lot. Why? I like the simple, stripped down nature of it, the light weight, and the quiet directness of the drivetrain. I don't think it's particularly dangerous...assuming you have brakes. I mounted only a front brake, which is more than enough. No brakes on the street is stupid. With brakes, losing control downhill, hitting a wall and killing yourself is idiotic...pretty easy not to lose control for me, YMMV. I trained for a century on the fixed gear bike on all kinds of roads, rides up to 65 miles long. Mine is geared to allow for climbing (But I have to work for it). This also means that on a long downhill section, I must manage my speed with the brakes. On shorter downhill sections, I can manage speed with my legs (interesting sensation and works muscles differently), or spin out to ludicrous rpms which forces you to have a smooth pedal stroke. Brakes are always there to stop you quickly if needed. I never unclip from the pedals and allow the cranks to freewheel...that's dangerous and compromises control IMHO.
Bottom line, fixed gear riding is different, fun, and safe if you're not an idiot. I recommend it.
Mine is a converted road bike...an old 3 tube carbon Vitus frame with purpose built fixie wheels, plus a bunch of parts I had lying around. This frame has vertical dropouts, so I used a White Industries ENO hub that has eccentric adjustment to deal with chain tension. It's an expensive solution, but I did not want a spring loaded chain tensioner since that doesn't work with fixed gear, only singlespeed setups. The ENO hub is flip flop, so I can mount a freewheel, but I have no plans for this as I like the fixed gear. If I want freewheel, I take the roadbike.