A brand of fanfiction
in which the author inserts himself into the story. In most cases, he has superpowers
and/or a Mysterious Past(tm), solves all the characters' problems, saves the day habitually and, of course, has the most desirable female in the show falling for him.
There are SI stories that are not written by 14-year-olds with a self esteem problem and no literary talent, and which therefore don't suck, but they are few and far between.