This is a great feature that Strava provides. They call it a segment, and essentially it's a route (or segment of a route) that you can pull out of one of your training logs. Not only can you see your performance on subsequent uses of the route, but others can find the segment and give it a blast too.
Actually, Strava is smart enough to do this automatically, so it's quite possible to be seen on the leaderboard with out actually trying.
Of course, you can make the segment private too if you don't want other people competing with you.