I don't really care to use a straw, but I know some people who do. One reason I'd never considered: if you have sensitive teeth, you can drink from a straw without having ice cubes come into contact with your teeth. The straw also helps the cold beverage bypass the teeth (for the most part.)

Also, some folks are worried about germs on the rim of the glass. Using a straw doesn't help you with any germs that might be inside the glass, of course, but I suppose extreme germophobes may use straws for that reason.