1: She is stunningly/unusually beautiful. Oh she may deny it, claiming to be a "plain Jane" and modestly deflecting any compliments on her looks, but everyone else in the story will be sure to drool all over her. Mary Sue is perfection incarnate - perfect hair, perfect eyes (the kind that "sparkle like jewels" or "pierce into your soul"), perfect skin, perfect figure, gorgeous gowns/snazzy leather warrior outfits, cool-looking weapons, etc...though she may bear a striking resemblance to the author of the story. And she sometimes shares the author's name (that includes middle, last, nicknames, acronyms, etc.) Mary Sue could easily be described as an "author's pet" or a self-insert.
2: She has multiple special abilities or skills (like she can somehow "wield a blade" really well without years of training and experience...unless, of course, she's been trained by the best since age four). There's nothing she can't do or excel at, everything gets handed to her on a silver platter, and her Speshulness knows no bounds. She could be a shape-shifter with Super Powerful Shiny Magic and a wow-the-crowd singing voice, or a genius computer hacker who can play the flute and violin, has a black belt in karate AND can recite encyclopedia excerpts on a dime, or a half-angel warrior princess who sends the Bad Guys buggering off just by going all "echo-y voice and holy light"...you get the idea.
3: Going hand in hand with the above, she's always being uber-heroic, rescuing random people and saving the day. The fate of Life, The Universe and Everything depends on her. Without her Speshulness to aid the Good Guys in the epic battle, the Bad Guys are sure to win and the world is utterly DOOMED.
4: She's kind and virtuous (unless she's an EVIL Mary Sue) and has no big character flaws of any kind. (And no. Clumsiness and/or a feisty temper do NOT count; they're far too generic and only serve to make her look "cute".) She's usually either a "sweet angel" type, "mysterious woman" type or the "rebellious princess" type.
5: At least one character falls immediately/insanely in love with her, and vice versa (usually the hottest guy. Go figure.)
6: All the good characters in the story just seem naturally drawn to her (especially children and fuzzy animals). She's popular where it matters. EVERYONE likes her. Except the Bad Guys, of course...as well as any unimportant characters who serve no other purpose in the story than to be annoying and/or jealous of her utter perfection.
7: Sometimes there is a prophecy or legend about her. Usually it says something about her Speshulness, an all-important destiny, Twoo Wuv written in the stars, blah blah blah...
8: She is portrayed as being cooler/more mature or more important/powerful than everyone else in the story. Though on the flip side, she could also be portrayed as the poor, defenseless, yet ever courageous damsel-in-distress. Everything's always either about her or her love-interest. She doesn't know the meaning of "teamwork" and she steals the spotlight from everyone else.
9: She often has a tragic/angsty/mysterious past and her love interest has to "heal her wounded heart" or something. If she doesn't have a tragic/angsty/mysterious past, she always finds SOMETHING to angst about...and of course, her Twoo Wuv always rushes to comfort her. Oy.