I only run clinchers, so I don't have too much to add here.

However, a lot of my racing buddies use clinchers when they train and tubulars when they race. The clinchers are good for training because if you are out on the road far from home, changing a flat is a piece of cake.

However, they like the feel of tubulars when they race, and so use them with their race wheels. Like what was mentioned above, tubulars allow for lower tire pressure because they don't run the risk of pinch-flats that clinchers do. They are lighter because they don't have tubes, and my friends swear by them in the corners.