One of the most memorably bad concepts/backstories I have ever come upon is one of my favorite stories to tell.
I had been running a Vampire: The Masquerade LARP for about a year, and whenever I recruited new players, I tried to instill upon them how important it was to have an in depth concept for their character. It drives both the drama and investment for your gaming experience. I met a new player named John, and gave him my usual spiel. He got super excited and said he had an idea, but wanted to time work on it. He said he would get back to me in two weeks.
Two weeks pass, and he has sent me numerous emails about how pumped he was about his concept. He had been brewing it for two weeks now, and he knew I would be really into it. It was the best thing he had ever come up with.
Finally, we sit down on game night to make the character. I tell him to pitch the concept, and by now, I am really intrigued by his enthusiasm. He smiles, slaps his hand down on the table and says "German. Brujah." I wait for more, he just sits there.
That was his entire concept.
I should note for the none Vampire savvy out there, Brujah is simply a clan of Vampires. It would be akin to someone in Pathfinder saying their concept was a fighter. It is also important to mention he was not trolling me, and was completely sincere.