1. The flanges on a clincher rim will cut the tire & tube easily when the wheel hits a pothole or other obstacle, causing a pinch flat. To compensate, clincher tires are typically inflated to a higher pressure for a given tire size & rider weight, resulting in a harsher ride, higher rolling resistance and more rider fatigue.
2. When a clincher tire is inflated, the air pressure spreads the flanges apart horizontally. Unless the rim has hook beads and an extra layer of metal in the horizontal part of the "U" (like this:
[_] ), the tire cannot be inflated to a high enough pressure to avoid pinch flats without blowing the tire off the rim. When a tubular tire is inflated, the air pressure compresses the rim radially, strengthening it. So the tubular rim can be made lighter than the clincher rim without compromising the durability and reliability of the tire and wheel combination. Here are some rim cross-sections to show what I'm talking about:
http://www.velocityusa.com/default.asp?contentID=563 . The "Escape" and the "Pro-Elite" are tubular rims, the others are clincher rims. Notice that the "Escape" is distinctly lighter than clincher rims of similar dimensions.
And yes, I'm told that tubulars are safer to ride flat and are less likely to be damaged while doing so than clinchers.