I built a fixed gear bike a while ago with only a front brake. Some fixies are brakeless, but I wasn't about to go that route. I felt perfectly safe and was able to stop just about as fast as if there was a rear brake since it's possible to have enough weight transfer to the front wheel that the rear wheel is not doing any braking at all.
The only time I would really miss a rear brake would be downhill on a sketchy surface where inadvertently locking the rear wouldn't be nearly as unstable as locking the front. This was never an issue on my fixie, but it could be on my regular road bike.