As far as here goes, we're about records of individual runs. If you want to compete here:
1) Find a game you want to compete in. Any format is good so long as you keep to . . .
2) The
rules. Stick to them or perish painfully :)
3) Use the Submissions button on your left to submit your statistics for the game you're competing in.
4) Lather, rinse, repeat if required.
If you're talking direct competition, that depends on the system. I believe there's a Genesis/Mega Drive proggie that lets you netplay, don't know about other stuffs though.