There is an old concept in SFF called the "Mary Sue/Gary Stu." These are characters which act as self-insertion and wish-fulfillment vehicles for the author. The phenomenon is originally named for a common element of Star Trek fanfiction.
But of course, this sort of thing is not limited to fan fiction. To a certain extent, a lot of main characters are vehicles of wish-fulfillment. Indeed, I use the obviousness of the self-insertion of the author as a sort of unofficial barometer of the "maturity" of a work of fiction. The more I get the feeling that a character is living out the author's personal fantasies, the lower the story falls on the rating system (this does not necessarily indicate displeasure with the story itself, though it certainly corresponds strongly).
However, the primary problem behind the Mary Sue/Gary Stu is getting muddied. We're now seeing it applied to all sorts of characters who have a variety of talents and seem generally all-round awesome. My problem with this conceptual drift is that the problem now seems to apply to just about every protagonist ever written.
We like to read about exceptional people. They feature as the main character in a helluva lot of stories. Even the quintessential "everyman" character generally has some extraordinary skill or manages to save the day due to a sudden (and often unlikely) stroke of genius. None of these necessarily merit the label of self-insertion.
In order to restore the trope to its original meaning (or perhaps to do away with that version of it altogether, due to some stick sexism-related issues) I've come up with the concept of Overcompetance.
This is meant to do away with the discussion on self-insertion. I don't really care about it, as I assume self-insertion is happening in some ways (the good authors just disguise it well). Thus all I care about is whether the range of skills and talents displayed by any particular character feels real. At the point where it begins feeling artificial, there begins a display of overcompetance.
Obviously this is a highly subjective assessment (as is everything else in literature). I generally ascribe it to characters who manage to miraculously "discover" several new talents during the course of a book. Encounter magic for the first time and you're already really good at it? Okay. Wait, you only just started riding horses and you do it as if born in the saddle? Hrm. Hold on, you've never held a weapon in your life and after a month with a sword you can best experienced soldiers? Sorry, that's one too many. You fail the test.