What is safer...coaster brakes, rim brakes, or fixed gear braking? I currently have a 'regular' bike, i.e. a bike with hand rim brakes but I've been more fascinated recently with single speed and fixed gear bikes. One of the reasons that I've held off on getting on is the braking.
How does coaster braking and braking on a fixed gear bike compare to rim brakes?  I live in NYC and want to make sure that I can brake in all situations!
A track bike (fixed gear) has no front or rear brakes.  You slow the bike down by resisting the turn of the pedals but you need to be careful to not push too hard, which can lock up the rear wheel and cause a skid.

But most fixed gears aren't true track bikes.  You should be able to find one that has standard brakes on both the front and rear wheels.  The front brake is especially important since that's where most of your braking power comes from on a normal bike.

A coaster brake is basically a drum brake in the rear hub.  Pedalling backwards engages the brake.

Personally I would expect a bike with a normal front rim or disc brake to be "safest".  Front brakes have much more stopping power because your weight shifts to the front wheel when slowing down.  Plus you can control the amount of braking power more easily by hand than by resisting with your feet.