Call me silly, and maybe I've been playing too much Dead Space and the like, but I think it would be a cool feature.
For those of you unfamiliar with the concept, New Game+ (or New Game Plus) means once you beat the game, you can restart from the beginning with your current character/stats/equipment.
There could be a couple of ways to handle this:
1. Only allow the character(s) that finished the game to use the New Game+ mode
2. Once the game is beaten, the New Game+ mode can be used to create a new character that starts at the highest level the game was completed at
This would enhance the replayability, as well as encourage people to complete the game at least once. For those hardcore players, an extra difficulty mode could be introduced that toughens up the enemies to keep things interesting, and maybe some special items/weapons/armor would only drop in the NG+ mode. It would also give the opportunity to experiment with some crazy gameplay ideas that you might not implement in a regular run-through.
I guess the biggest concern with something like this would be the impact on programming and the editing tools... it might have to be relegated to something a bit more simple that what I've imagined to be able to implement without consuming a large amount of development time.