First off, who is Mary Sue? Mary Sue isn't a person; "she" is a set of characteristics. Let me show you an example of a Mary Sue story:

Once, there was an Invader known as Maue.

She was the strongest, smartest, and most beautiful Invader ever!

All men, even guys like Dib who have no interest in girls, instantly fall to their feet when they see her, and do whatever she wants. Why? Because she's Maue, and thus, whatever she wants, she gets.

Girls will go gay for her, she's amazing, and even if she's threatned, the universe shall become unstable.

THE END

That, dear reader, was a Mary Sue story. These are the key things seen in your average Mary Sue:

Strength: Now, it's good to have a strong character. But, there is such thing as too strong. You don't want your character saving the day every damn time.

Intelligence: I'm not saying your character should be an idiot. I'm simply saying they shouldn't be ridiculously intelligent. They shouldn't know absolutly everything or, and this does happen a lot, automaticlly figure out that Zim is an alien. Remember people, this is the Invader Zim world. Amazing intelligence does not exist. But, if your character is human and you want them to figure out Zim's secret, then make it happen overtime, with a reasonable amount of proof to back it up.

Beauty: This is the most common Mary Sue flaw. It's ok to make your character pretty, but you don't want her to have overwhelming beauty. Here's how both types of beauty sound:

Normal beauty: She had long, dark red hair with streaks of brown that fell to her shoulders. Her eyes were a very simple blue, but they were pretty all the same.

Mary Sue beauty: She was a true beauty! She had long, golden hair that reached her waist and shinned elegantly in the sunlight. And her eyes! Oh, what a sight they were! One eye was silver and sparkled! The other was golden and also sparkled. She was beautiful and anyone who looked at her instantly had the urge to sing and go skip in a flowery meadow.

See the differance? Mary Sue beauty can get rather annoying. Keep it simple. To sum it up, don't do a Twilight vampire.

Instant love- This is another common flaw. It's ok to have, like, one or two guys love your character. But you don't want every guy on the damn planet to be in love with her. It gets rather annoying and you lose readers. Also, don't have characters who aren't really interested in girls instantly fall in love. Characters like Dib and Zim are the type who are more interested in their work than girls. Remember to take it slow.

Getting what they want- Don't have your character always get what she wants. For example, if your character is an Irkan who want to help Zim take over the world, don't have Zim immediatly say yes. Zim is more of a lone wolf, and isn't the type to accept help. Same with a friendship with Gaz. Like Zim, Gaz is a lone wolf and not the type to talk to people. Both of these things take time.

As you were reading this, did any of it sound familier to you? If it did, think about your character. Remember, no one likes a Mary Sue.