Can you run in Minecraft?

I've seen a lot of people on SMP that seem to go faster than me when playing. Did I miss a run button that I'm not aware in the game?

As of Beta 1.8, you can sprint by double-tapping the forward key (W by default). This seems to be unlimited, as long as you don't let go of the button and don't run into anything. Hitting a mob while sprinting will also cause you to stop sprinting, and send the mob flying.

Your food meter drains a lot quicker while sprinting, and when it's down to 3 pieces of meat or less, you can't sprint at all.

Old answer, preserved for posterity:
Not currently, no. The people you saw were probably either lagging (and their delayed position update caused them to look like they're running) or using speedhacks.

Although, notch has toyed with a sprint mechanic, so it's possible that this will be added in a future update.