As both an artist and a writer, I am always told to be aware about creating a "Mary Sue".
If you don't know what a Mary Sue is, she/he is an idealized character representing the author. A Mary Sue is an ultimately perfect character, lacking in realism to be even remotely interesting.
Mary Sues are often found in fan fiction (Marty Stu being the male counterpart). For example, Harry Potter Mary Sues are, or were, some of the most common Mary Sues in fan fiction. The characters were described as beautiful, intelligent, knowing magic way beyond her years, having every character in the series fall in love with her, being undoubtedly witty, and often being a characters relative (i.e. snape's daughter, dumbledor's daughter, harry's unknown sister etc.)
Mary Sues are often created in place of the author, which is why the author bases her Mary Sue on herself. Everything that happens to the Mary Sue is subsequently happening to the author, in the author's head. I have seen One Direction fan fictions where the character happens to meet the boy band, then have basically all of them fall in love with the characters. Now who wouldn't want a bunch of famous boys fauning over you? That's the reason authors often write fan fiction if they are not shipping characters together.
You can often identify a Mary Sue by her name and occasionally the way she is described, but that's more of an artistry thing. If a character has a name that wouldn't often be a name, (like Flower, Chaos, Dream) and/or a crazy spelling of a simple name (like Kathyrnne instead of Kathrine, Ulissa instead of Alyssa, Haylea instead of Haley) you might have a Mary Sue on your hands.
If you'd like to check out some comics regarding Mary Sues, you can find some here:
http://piratemonkeysinc.com/ms1.htm
Ensign Sue Must Die, where I got my cover: http://comicalclare.deviantart.com/gallery/25413573?offset=24
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The Mary Sue Diaries
Non-FictionA guide for writers everywhere on character development, and how to avoid the Mary Sue.
