Elbows and Knees are the hardest bones as weapons, so they are most effective at delivering the type of hard blow needed to cut. If you are looking for a cut to END the fight, it is usually above the eye or on the skull. The latter type of blow is usually illegal. Headbutts are effective, but usually illegal -- but even an accidental headbutt can open a major cut (this is how Couture took command of the fight against Victor Belfort in UFC49).
The best places to open a cut are where there is the most bone and it is the most protruding because this is where there will be more friction to cut the skin, and where the skin will be the thinnest. I am not sure how useful this information is in a fight though; for instance, usually when you are throwing elbows down at someone's face, you are just looking to land shots to the face, perhaps a particular side, not specific points. This is because your opponent will be trying his hardest to avoid those hits.
In my experience most times when someone gets cut standing from punches, it is a bloody nose and it will not stop the fight. Usually fight-stopping cuts happen in the clinch with elbows or knees, or by elbows from the top on the ground.
