Do you know what Fixies are? Fixie is a short form for fixed-gear bike, meaning that these are single-speed bikes that have no free-wheel mechanism. The faster you pedal, the faster you are. If you pedal backwards, you also ride backwards. You can't stop pedaling though, cause otherwise the rear wheel is blocked. Stopping and slowing down is much more difficult than on a usual bike, mostly done by skidding.
Fixies first appeared in track bicycle races. Then bike messengers picked them up. Nowadays everybody who is particular about one's appearance wants a Fixie. It's state-of-the-art, although not really practical for most people. But if you still want one, you should check out Fixie Inc. (cylces for heroes) or pay the Citybiker a visit (Bobo bike shop in Vienna 1070).
I don't have a Fixie. I'd love to try and ride one though, just to know what it's like. But it wouldn't be really useful for me since I live on a hill (Vienna is quite hilly in some areas) and I would never make it up and down there with a fixed gear. Well, uphill wouldn't be such a problem (I've even done this with one-gear Citybikes although it was a pain), but downhill would be because of the braking thing.
Wanna see a short movie about Fixies in Vienna? Well, then check out "Wien fixiert" (in German). You also get some impressions of Vienna itself. Enjoy it!
By the way, I've seen the premiere of this movie at the Bicycle Film Festival in Vienna last October. The festival was really awesome. I'm already looking forward to the next one :-). If you get a change to see it somewhere close to your place (it's a worldwide festival), don't miss it! Otherwise, check out the website for a few movies. They also sell some of the filmlets on DVD, don't know if online though. There's even some time left to submit a movie yourself - for this year's BFF the deadline is on the 7th of March 2009.