Follow these links to go to free online running games. Some are more humorous than "competitive."

Moron Marathon: My personal favorite; pick a character and a race. Compare your success to other gamers. Faster you go, better you are; but be careful, go to fast and you'll "smash" your character.
http://www.onlineflashgames.org/3-sport-games/2199-flash-game-moron-marathon/play.html

Presidential Olympic Games: Competition heats up between Presidential Candidates.
http://www.flasharcade.com/arcade-games/presidential-olympic-game.html

1200m Relay: Snap,Crackle, and Pop Style
http://www.onlineflashgames.org/3-sport-games/1286-flash-game-1200m-running/play.html

100m Sprint: Fun game in which you are the sprinter. Advance your way from lower levels to elite competition.
http://www.gamedesign.jp/flash/sprinter/sprinter.html