The more practice you get, the less annoying the putting on/taking off is. By now I can pop them in and pop them out in 2 seconds. They're convenient for sports, esp contact sports, won't get your glasses banged around. They give you a better range of vision, because for glasses, you only have the centre part of your visual field that are covered by the lens, while the contact lens follows your eyeball movement.
Thirdly, which I think is the most important, is that the worse your eye become, the heavier glasses get (even with the newest featherweight lenses), and with conventional glasses you get this "tunnel vision" where you only get the clearest vision if you're looking directly through the middle of the glasses. With contact lenses, this problem is eliminated since, again, the lens follow your eyeball.