How do you delete a game on your multi-player list once it is over?

Should automatically delete. Maybe it's just over for you:)

You have to change your filter settings under the options button at the top of your games list.

On the My Games page, click Options and then change your filter to "Active Games." This will make it hide games that are finished.

Finished games are not completely deleted - this way, you can always change your filter back and find them so you can go review past strategies.

Thanks!