If it's a freewheel, it's called singlespeed. If it's a fixed hub, like a track bike, that's a fixie or FG. The hipsters ride track bikes brakeless, smart people add at least a front brake. Mine has two brakes; so far I've not been able to skid or skip the bike to stop it. The speed control on a fixed hub bike is awesome. You can maintain an even speed while riding next to somebody walking. Most bicycle makers, including Masi, have street-friendly SS/FG bikes.

I have a Bianchi San Jose SS/FG cyclocross bike. The rear hub is fixed/free but so far I've only ridden it fixed. If I were riding trails or going on a long(30+ miles) ride, I'd flip it to the singlespeed side. I ride this bike when I'm riding with my wife or my granddaughter; much easier to maintain their pace. It's also my commuter bike, with fenders and a rack.