Superheroes Wear Capes. This is a given.
A cape has the obvious effect of making the wearer look larger and more imposing. Artists often use them as a way to make characters look more bad ass. (Just look at Batman over there; he wouldn't look half as awesome without his cape.) The reasons for this are many. The color might provide a counterpoint to the rest of their clothing, or else blend with them to give the wearer a dynamic silhouette. In the right conditions they can wave in the wind and look dramatic and striking.
But the main reason for this is that, in the days when circuses were common, the strongmen often wore tights and a cape. This association was made by Jerry Siegel and Joe Shuster when they designed Superman, the first superhero ever.
This can apply to any character, whether he be a superhero, supervillain, a sidekick... heck, it doesn't even have to be a character in a superhero setting. (Look at Darth Vader and his bad ass cape.) This can also count if the actual cape has some sort of abilities in and of itself, making the cape itself a bad ass.