[li]Having Bart Simpson run away from home and hook up with a teenage runaway[/li][/list]
Didn't this actually happen in a simpsons episode recently, because I swear I saw something really close to it.
The show may have done something close to it. (The episode where Bart escapes from Juvenile hall with Sarah Michelle Gellar sounds fairly similar.) But the tone of the fanfic was much different than a Simpsons episode.
See, back in the ancient past (back when Bill Clinton was President), the Simpsons fans who wrote fanfic seemed to not get the whole "Simpsons is a comedy" thing. A large number of them wrote fanfic for the show as if it was a drama. Or, more accurately, a soap opera with the appropriate amount of melodrama. The plot for that particular fanscript went like this: Bart has a big fight with Marge and runs away from home and convinces Milhouse to do so as well. They hit the road and run into two female runaways (who were around 16, IIRC. Bart was still 10 or so.) and they all fell in love. Marge catches up with Bart, they fight again, and Bart storms off, changing his name and never again associating with his family. The end. I'm pretty sure that the actual show would have a slightly more upbeat ending.
I'd direct you to the actual fanfic, but unfortunately in the late 90s and earlier in this decade, Fox had a nasty habit of sending cease & desist letters to Simpsons fanfic sites, resulting in them dumping their archives and also resulting in a lack of fanfic from that era on the net. And I neglected to save a copy of this one after finding it.