Capes were once quite common among superheroes. However, they have fallen out of favor in recent years because of a string of high profile fatalities, as shown in the groundbreaking documentary The Incredibles.
The dictionary defines a cape as "a piece of land jutting into the sea or some other large body of water." From this, we can see how important capes are in the world of super heroics.
The first superhero to wear a cape was probably either the Shadow or Zorro, depending on which one was published first. We want to say Zorro, but we're simply not sure. It's times like this that we really lament the absence of a massive knowledge database that can be accessed free of charge and takes advantage of the pooled knowledge of its users.
There are some people who would argue that neither Zorro or the Shadow count as superheroes anyway. These people clearly aren't familiar with the Davey-Mitchell Standardized Superhero Determination Test (DMSSDT), which can determine whether any fictional character is actually a superhero. The essential part of the test is reproduced below.
1. Are you dressed like an idiot?
2. Do you insist people call you by a stupid name that you made up?
3. Do you have freaky powers or lots of money or big muscles?
From this, we can see that the Shadow and Zorro are clearly superheroes, as are Elvis Presley, Michael Jackson and The Situation from Jersey Shore.
The first superheroes to make appearances in comic books were Superman and Batman, both of whom wore capes. A rash of imitators soon followed, but we're going to ignore them entirely and pretend they never existed. Therefore, the next superhero to be created was the Flash, who wasn't given a cape. Presumably this was because the writers were afraid he would trip on it. However, some scholars believe it's because the artists figured they had already done enough to make him look like an idiot, what with giving him the world's most ridiculous hat.
Little known fact: The Flash originally developed super-speed to escape cruel taunts regarding his helmet.
After the Flash came Wonder Woman. She didn't have a cape either, as it would have at least partially obscured the view of her ass.
This wasn't so important by the 1970s, as TV allows for jiggling.
The next major hero from DC Comics was Green Lantern, who had a cape. The thinking at DC Comics in those days seems to have been "flying = cape". Meanwhile, the company that would one day become Marvel Comics didn't make this conceptual leap, instead choosing to make characters fly by setting them on fire or gluing ridiculous looking wings to their ankles.
Capes have garnered a reputation for being dangerous in recent years. This probably started with Watchmen, where a character gets his cape caught in a revolving door and is brutally murdered. The blockbuster hit film The Incredibles developed this theme in considerably more detail, essentially sending the message that capes invariably destroy the hero. This is kind of weird when we actually stop to think about it. Another character in Watchmen is murdered for being a lesbian, and Disney and Pixar haven't said shit about that.