Are there any websites for keeping score of various boardgames?
Boardgamegeek (http://boardgamegeek.com) has a play reporting feature which can include who played, what position each played, their score, and additional notes. Play notes can be publicly accessed. (It can be a bit of a pain, tho, to find someone else's plays.)

It does exactly what you're asking for. If the same person reports every time, it's readily viable to find it.

Further, one can create a private geeklist which lists the games, instead of using the play reports feature.