The bastard child of a fanfic, and an AMV, a songfic is a fic "set to music." They are usually written by crazed fangirls in order to show both the superiority of Linkin Park and their chosen OTP, whatever that may be.
They usually take the following form:
It starts with one thing
I don't know why
It doesn't even matter how hard you try
Keep that in mind
I designed this rhyme
To explain in due time
All I know
Luffy stared sorrowfully at the ground. They had been travelling together all this time, and yet Zolo still seemed completely oblivious to his advances.
Time is a valuable thing
Watch it fly by as the pendulum swings
Watch it count down to the end of the day
The clock ticks life away
It's so unreal
Et cetera, et cetera.
Joss Whedon (yes, he incorporates all aspects of fandom) popularized songifcs by writing one of his own in Buffy the Vampire Slayer's sixth season. Entitled "Once More With Feeling", the plot involves... oh hell, you've either seen it or you're going to.