When I write a fanfic, or any story for that matter, the characters all have certain traits similar to mine, but I don't consider any of them self-insertions (except for two SI's that I created, but we'll get to those later).  Like Zephyr is a bit sarcastic, Petra is...well, she's Petra, Vega is sarcastic also, Sora and Aoife are hyper, Spica is a genius (literally), Seiki is a feminist, Ferio is bitchy (as I can be sometimes, though not 24/7 like she is), Apollo (from my play) is a smartass, Artemis (also from the play) is a bit anti-male and so is Amalthea.  And I left out lots of them, but just about all of my characters (except for Aidan and Mariah/Io) have a little bit of me in them.
I did create two self-insertions (characters that are, basically, the writer as a character in the story).  One of them was for Astros, and that was the infamous Shizuka Kiko/Sailor Corona.  I made her like me, that is, how I was like at the time (I'm not such a wimp anymore, tho).  She had both my good points (like what?) and my flaws.  And that is how self-insertions should be.  I'm not saying I'm the expert and everyone must do as  I did, but I'm just saying your Mary Sues should be balanced characters just like any other character.
Know what annoys me a whole lot?  Well, you can probably tell what I'm going to say based on the topic of this article, but I'll tell you anyway.  It's all-powerful, Miss or Mister Perfect self-insertion characters.  The writer calls it a self-insertion, then just takes away all the flaws and there you have it!  A self-glorifying fanfic!  Usually sticking those characters into a storyline insures that there will be no plot and none of the characters except for the self-glorification character will get any development (if you're lucky, and maybe not even they will).  So then, the elements of the story aside from the Mary Sue deteriorate and we're left with, basically, a self-promotion piece.  I HATE THAT!  Also, it would be wise not to have your Mary Sue have a love interest.  That seems a bit self-glorifying too.  And by no means shall you give them multiple love interests and make them a guy or girl magnet.  Basically, don't write your story just so your character can get together with a character you like.
What you have to do is give your character all your traits, flaws and all.  If you're too proud to write yourself in character with all your bad points as well as good, then don't do it.  Please, just don't.  Don't write it and save us readers from another monster inflicted on us.  The Claris Project is good in this sense because she's, to put it her way, "the anti-Mary Sue".  Instead of glorifying herself, she puts herself down.  I'm not suggesting you do that and constantly bash yourself, because that can get annoying too (heh, yeah, like I should talk).  But for the love of Utena, people, give your characters flaws!  Create them as you would any other character and make them balanced.  You wouldn't normally create a perfect character who always wins, so don't do a self-insertion who does.  It's just tacky.  Also, don't just create any old character, then say it's a self-insertion.  Even if it does have flaws, if it's not you, it's not a bloody SI! *breathe in, breathe out* Ooooookay...  Let's do some case studies, shall we? *evil grin*

Case study 1: The Gorzog-5 Trilogy (now down)
Damn, I wish this was still up so I could do a review on it. *curses in multiple languages and dialects* Anyway, do NOT, by any means, do what this fic did.  All the characters were based on the author and her friends, and they were all perfect little stereotypes.  She said she originally had another character, but he wasn't based on any of her friends and "didn't have much character development"...hmm, what does that tell us?  That she can't create characters for the life of her?  Uh, yeah.  Not that any of the others had development either.  And her own self-insertion was the most annoying creature to grace the planet, even more annoying than Togepi.  She was basically little miss perfect, the "youngest senshi" (she was 13, so no, Chibi-Chibi is definitely younger), and for some reason she went to a special high school where only gifted people went or something like that.  Also, she created sailors for Neptune, Saturn, Uranus, and Pluto, which you just DON'T do.  Okay?  You just don't.  Oh, and look at this!  Her Mary Sue was the only one with a decent profile, the rest of them just had little statistics and nothing else!  The fic was crappy too.  I couldn't get through it, it was just SO boring and pointless and UGH!  The pictures were good, but obviously traced.  Blah.  Talk about your self-glorifying piece of shite.

Case Study 2: A Tricky Situation - Touch and Go
Two of the main characters are self-insertions, but they're fairly good ones.  Oh yeah, did I mention that this is an absolutely BRILLIANT fanfic and that everyone must go read it now?  I didn't?  Well, I'll get to that part.  Anyway, the character Starr I have no problem with, because she seems more human.  Faris, however, seems a bit too...perfect.  Sure, she has flaws, they're in there too.  But her good qualities are too numerous and too emphasized in the fic.  And she always wins, and bunches of guys fall for her.  Well, maybe not bunches, but a few.  More than one, anyway.  And she meets Mewtwo, who is apparently her "equal."  The most powerful Pokemon is her equal?  Uhh...right.  The fic is great, honestly, but Faris just...bugs me in that way.  But you'll see more of that in the review I write of this.

Case Study 3: Sailor Astros
Yes, this is my fic.  I wrote a self-insertion for this, the aforementioned Kiko.  I didn't like her very much.  She was too wimpy.  Sure, I was too at the time I created her, but now that's really outdated.  She looked quite a bit like me, except for her being an anime character and all.  And she was pretty balanced too, in my opinion.  But now she lives on the cutting room floor, along with Chibi-Mika (yes, she's leaving), Kiko's "sister" Mizu (if Kiko goes, Mizu goes too), and yes, Shisou/Sailor Earth (pointless character).  Why is this, you ask?  I was creating too many unnecessary characters.  Kiko and Mizu had no real purpose in the story except as two more senshi for me to dabble around with, and I kept insisting that I needed Shisou in the story until I realized that she could be basically dropped from the series and no one would notice.  And that's what I did, and I'm glad I did so and they won't be back.

Case Study 4: Pokemon Neo
My other self-insertion,and the more current one also.  The Mary Sue in this one is Ruairi, the Chartreuse Gym Leader.  She's fairly true to me.  She's hyper and friendly and smart, but she has obsessive-compulsive disorder and negative self-esteem (no, I'm not obsessive-compulsive, but the self-esteem part is true).  She's also very up-front and slightly bitchy, but then all of the girls in this story are, and all of the guys are wimps.  Although she doesn't look a lot like me (lavender hair and green eyes, and the typical anime-style proportions), her personality is true to mine and hey, we even have the same favorite Pokemon types (dragon and psychic).  So in other words, I think she's a lot better than Kiko.