War of the Ring is looking enticing to me. It models a lot of the situations and possible situations from The Lord of the Rings, with two victory conditions for each side, one based on territory gain, the other based on Frodo successfully or unsuccessfully making his way to Mordor with the Ring.
I've played LotR Risk, which was fun -- definitely more so than regular risk -- but still relatively disconnected from the theme on which it is based.
Then, of course, there's Lord of the Rings, which moves very quickly and can be a lot of fun. "Hey, I was killing Shelob!"