Toe clips (or clipless) are a necessity IMHO. It feels ******** to try to slow down on a fixie without them.

Not to mention you could easily lose your footing. I have a friend who is adamant that his Alpha Mercury came brakeless and that it was made for the velodrome and refuses to put toeclips on despite his obvious disability to slow down (bouncing, bumping, losing footing, jostling, etc.) and a garage full of great parts. He looks like a complete jackass, and acts like he's a god even though he can't even skip stop his 12-speed. I don't even know why he keeps whining about how "it's not that cool to have a fixie" even though I've wanted one long before he decided he wanted one and got the first one he saw on craigslist for under $300 a week later.

That's my rant. In conclusion, don't ride without clips even if you have a brake or two. You'll hurt yourself... and look like a jackass.