Mary Sue

A Mary Sue fanfic is in which the primary character is an analog for the author, its abilities inflated to an abnormal level in a way that outshines all other characters. The phrase had its origins in Star Trek fanfiction. It is usually considered a pejorative term, and Mary Sue stories have a bad reputation in most fandoms.

A Mary Sue story in which the author appears as himself/herself, by name, is called a self-insertion.

In Daria fanworks, several authors have distinguished themselves by writing Mary Sue tales that are very good. Angelinhel ("An Angel Named Mary Sue"), Medea42 ("The Slacker Within"), and Scissors MacGillicutty ("Where's Mary Sue When You Need Her?") have done outstanding work in this area. Mary Sue stories can double as metafiction if properly done (per the stories noted above).

Compare with Tuckerization.

Examples of Mary Sue Daria Fanfic
These might be good examples, or they might be bad ones. You decide.
 * Self-Insertion, by TAG
 * Small Worlds, by TAG