A "Mary Sue" or "Gary Lue" - obviously the same thing, the name simply changed to refer to whatever gender is considered this - is a perfect or nearly perfect character.

Have you seen people who will join a role play and their character is basically god's gift to the world, pardon the phrase?

I mean this as in the character, starting out, is beautiful, pretty, handsome or has 'fine features' or something.
This is their first mistake.
Never, ever, under ANY circumstances use 'Beautiful', 'Handsome', 'Pretty', 'Cute' or even 'Ugly' to describe your character. Just don't do it.
Do you want to know why?
Because everyone has their own opinions.

Just because YOU think your pet is beautiful and attractive, that doesn't mean everyone else does. Heck, some may think your character is butt-ugly and unattractive in their personal opinion, and here you are describing it as 'beautiful'.
Likewise, you shouldn't use 'Ugly' either, because perhaps you are using a grotesque character, but others may find it perfectly normal or attractive even.
If your pet was 'beautiful', then it HAS no real look; it is simply whatever anyone would want or CONSIDER 'beautiful'; therefore simply having a perfect quality when it comes to looks.

See? It's just simply not done..or, it shouldn't be.
You should be able to have your own character SAY that the other looks good; not have to read them flaunt about how handsome and attractive their character is. For example...this.

Incorrect

Player 1: A stunningly beautiful teenage girl walks down the park trail, her long blonde hair flowing gently behind her and her light blue eyes cast downwards at her feet, almost seductively.

Player 2: A tall, rather lanky boy of about seventeen stood against a tree, leaning there boredly. He glanced up over at the path that ran through the park, noticing a girl nearing him.

See? What's the point? There's no longer a reason for Player 2's character to even say anything about Player 1's character, since apparently, she is 'beautiful' and must be /everything/ he would like in physical features.

Now, you can easily say something like the tiny pup sat up on his hind legs, folding his front paws at his chest in a begging motion and looking up at the other with his cutest possible expression", because you are saying he is TRYING to be cute; not that he IS cute, since not all may like puppies, and obviously, not every single person on this earth is going to find them 'cute'. Some people hate animals and canines, so therefore..they may not even find it remotely adorable.

Now, for a more correct version; try something like describing your character's physical features. Use adjectives and a lot of words that are very descriptive; such as Lanky, Dainty, Thin, Slim, Tall, Short, Muscular, or even describe how tall your pet is in feet and inches and stuff; or how much it approxomitely weighs and so on..but seriously, if you say "Beautiful" or "Handsome", how does that give anyone a mental image of what your character looks like, other than something ANY reader themselves would be attracted to? See, it doesn't make all that much sense. Here's a better example of this.

Correct

Player 1: A tall, thin and rather dainty teenage girl walks down the park trail, her long blonde hair flowing behind her and her light blue eyes cast downwards at her feet, almost seductively in a shy, flirtish manner.

Player 2: A tall, rather lanky boy of around seventeen stood against a tree, leaning there boredly. He glanced up over at the path that ran through the park, noticing a girl nearing him. He couldn't help but stare for a moment or two, before quickly casting his gaze away so as not to appear rude...she was quite pretty, in his opinion.

See now? That's their personal opinion! ^^ Their character thought the other was pretty; and in return, Player #1 can also describe Player #2 as Handsome, Charming, Alluring and so on. See? It works both ways.

This also goes for 'literacy'. This means how good you are at role playing, in RPer's slang. For example, if you are considered 'literate', then it means you are descriptive, your posts are not abnormally short nor are they boringly long; and you use correct (or nearly correct) capitalization, punctuation, grammar and english.

Now, for example you can only be truly 'literate' if you see OTHER people telling you that you are.
Usually, if you are simply a "Self-Proclaimed Literate", meaning that YOU consider yourself a very good role player; then it very rarely is true. I, myself, have people commenting on my posts left and right (and yes, this is bragging) but that is also the reason I made this site.
If so many people apparently enjoy my skills and love to write, why shouldn't I share my knowledge with others? It's only polite, if you ask me; to at least help an RP-Newbie out and get them on what I consider the 'right track'. ^^

Anyway, back to 'Perfect' Characters.

See, it's not just saying how good your pet looks anymore..it's almost everything about them.

Some characters are defined by this as being abnormally smart..and I don't mean intelligent, I mean they just HAPPEN to know everything about everything. This, my friends, is what I like to call a know-nothing know it all; who, often, if your character has done something once, this one has done it twice and better.

Again, I ask you..what is the point? If your character is so smart, how could it have any friends? How could an average joe hang around with someone who constantly belittles him and treats him as a lower being because his role player has made him equal to the average person? It's just very difficult to relate to someone who is constantly,
"Hey, have you ever been snowboarding? I went once." "Of course! I go up to my own private little resort blah, blah blah with my own special snowboard that is worth $blah.blah dollars and I can do a [insert trick name here] and a [and again] and I can also do a [insert every sport's trick and etc. here as well...]"

See? I mean, come on. It's just no longer fun when your character is absolutely perfect.

And nom looks and intelligence is NOT just considered 'perfect'. For example, physical shape and so on. Say two characters are in a race. The first one is your average, run-of-the-mill who likes racing for fun, and even though winning is fun as well, the person role playing him hasn't made him into some ham who must win and will even godmod for him to to it.

Player 2, however, well..their character is perfect in every way possible here. I'll just show you.

Incorrect

Player 1: A young krawk ran across the ground as fast as he could, racing against a few other contestants.

Player 2: A tall and muscular kyrii dashed across the track, speeding past the other contestants and the krawk with incredible ease. In moments, he was at the finish line, tearing through the beautiful red ribbon and skidding to a stop as the croud congratulated him for leaving the others in the dust.

See? Come ON, people..what's the point any more? That's how all this incorrect stuff ends up, doesn't it? Pointless.

Who in their right mind would want their pet to try to befriend someone who is constantly faster, smarter, prettier, nicer, kinder, more attractive, stronger, more noticable, cuter and all in all, better than themselves and everyone else? It's basically impossible. I mean, come on; by then, it's just rude and they're only doing it for attention. This is how they attract 'despies', which is basically a lovesick role player who only role plays their characters to simply get romance and nothing else. Now, I'm not talking about having a flirty character..I would personally encourage that, since it can make the role play more interesting; but I mean all-out "made for each other" and "soulmates" kind of thing; where one girl will follow every guy around like a lost puppy. It's pathetic. -_-

But still, I see no point in having a perfect character. It's like, "Oh, my parents are gods so I own a castle and a giant city and I can win any race and kill any creature with a swipe of my paw and blah, blah, blah, blah, blah.."

Again, I ask you..What. Is. The. Point?
There IS none. You are no longer allowed a decent plot, since ANY challenge you come to, well..just let Player 2 take care of it, since they have absolutely no flaws. Coincedentally, they will never be caught stealing and they can escape or just AUTOMATICALLY SENSE /any/ trap in the entire thing; therefore completely ruining someone's idea. It's just no longer fun then, if you ask me.