According to Wikipedia, it is in reference to "oven cake" which was used to clean out the brick ovens when too much soot and creosote built up; therefore she was saying "Let them eat crap," because she could care less about their hunger.
As the phrase has been misunderstood, many believed that she was saying, "Let them eat cake"; meaning, if they have no bread then let them eat cake, as her wealth and privilege did not allow her to understand that if the poor could not buy bread then they could also not afford cake. Because of this understanding people not of the bourgeoisie refer to the upper class as "cake eaters", people who are so wealthy and clueless of the difficulty that being poor can bring.
Angelina: "God Paris, you're such a cake eater!"
Usually used as a derogative term for calling a person of wealth a spoiled 'you have it too easy' piece of shit brat!
Usually called to rich kids who drive BMWs and Mercedes-Benz's and get their college and college housing totally paid for and also get a hefty monthly allowance that's so great that they have absolutely no need to work in order to maintain their lavish lifestyle. This is a cake eater.
Synonymous with calling someone: Spoiled rich little fuck!
Tim: "Yeah, but dont worry about that cocky fucker, he's just another cake eater!"
It is now used as a nickname for all people who live in Edina, MN. Although meant to be an insult (for the dominantely white, rich, and stuck-up high school), many students from Edina now take pride in it. Example: An Edina sports shirt that read, "Cake: Breakfast of Champions"
This term is most well known by its reference to Edina native Adam Banks in "The Mighty Ducks."
Minneapolis kid: "Shut the fuck up before i rip you to pieces you fuckin cake eater"