Not so much modding, and it's not a game, but my AppGameKit app allows people to create settings and values that they can share with other users and load. At the moment it's done with QR codes and the data saved and shared is stored in an online database. With the new URL schemes introduced in the October version of AppGameKit (I've not yet tried) I'm going to look at also allowing them to share URLs which will do the same thing as the QR codes, just a lot easier.
This could easily be applied to a game, and used for sharing user designed levels (even the current QR code approach), but it does rely on a central database with all of the data created by each user.
