As neteon said, this is the single most important piece of advice in this thread.

To throw in my two cents, the very fastest way you can possibly stop on an upright bicycle is by sitting the furthest back on your seat and applying the front brake until the rear wheel barely begins to lift. That is putting a huge amount of normal force on the front fire due to the torque from braking, so unless there is lose ground you really aren't going to be losing traction. If you want to use the rear brake you have to let up on the front.

I've only braked like that twice, and honestly it's because I wasn't paying enough attention. The other posters have mentioned that you want to keep the rear wheel on the ground so you can brake with it and I completely agree - not because it helps you stop faster (though the difference in stop distance would be really close) but because you have more control over the bike with both wheels on the ground.

Generally, with two wheels you can either turn hard or brake hard, but not both.