You've been able to share user-created content on several games for the 360. Halo 3, Timesplitters, and a foliage-heavy shooter whose name escape me. Maps created by users, generally, with very limited toolsets. All from other 360 users (none from PC or other platforms). There were lots of these things, and each was rated by the users who'd downloaded it (to help you sort the wheat from the chaff). I never got into it much myself, partly because I didn't like those games, and also because I knew the tools were so limited. Halo 3 seems to have taken it the farthest on the 360, but I've never played it so can't comment.
I'm much more interested in PC mods being ported into the 360, rather than 360 users (unaccustomed to this) trying to create stuff with stripped down toolsets. MS is so tight, though, I wonder if they'll allow it. I am fine with them charging for it. I hope some of the money would make it back to the creators of the mod.