Since I like comics and history, let me explain those individual cases and then answer your question.

For Batman, it was functional as it helped communicate his connection to a bat and was integrated into his symbolism. The cape really does look akin to a bat's wings once unfolded.

Superman's creators Siegel and Shuster were inspired by the tights and bright colors of circus strong-men and acrobats of their day because those were their supermen, and those guys wore flashy tights/capes.

Thor's cape is accurate as that is how he is generally depicted.

http://en.wikipedia.org/wiki/File:M%C3%A5rten_Eskil_Winge_-Tor%27s_Fight_with_the_Giants-_Google_Art_Project.jpg

And for Robin, Bats have wings right? Well so do birds. His cape is for the same reason as Batman's.

But the root of your question really is, why are capes worn at all in works of fiction? The origins of a cape as an article of clothing apart from a shirt or jacket comes about with the cloak, which is meant to shield the wearer from the weather. However, it became really well integrated into society as a cape added a flair of drama to whoever wore them thus birthing our modern sayings like "cloak and dagger". Ever hear about the old sage wrapped up in his cowl or the valiant knight and his cloak which distincts him? The cape adds to the "character" of a character and is hence useful. A more modern example would be in A Song of Ice and Fire where the city guards for the capital Kings Landing are called Goldcloaks. (minor spoilers) That is both a reference to how prestigious they are and foreshadowing as to what truly buys their loyalty.

If your really want to get your cape knowledge on, this is what you want to read. http://www.fashion-era.com/Coats_history/cloak_costume_history_1.htm

hi! there's room for more info on this, but you can get started on responses to this earlier question

Why do classic superheroes wear capes?