Please note, that this is just an example of a classic Mary-Sue. I am not saying that if your OC has these traits, they are Mary-Sues. This is just a small example to keep in mind while creating an OC. This is not an actual character. Apologies if I used a name the same as your OCs, please just ignore that. To help you out if you're a new writer or don't understand the way Mary Sue works, I've written some additional points below which will help you out.
Kirei Aiko (きれい 葵子 meaning "beautiful lovechild").
Background
Kirei Aiko is a child of Uchiha Sasuko and Hyuga Hinato. Her parents moved out of Konoha when her mother was pregnant and moved to The Land of Mist. When Kirei was 5, a shinobi came and attacked them. Her parents were killed, and she was the only one left alive, because she defended herself using the Eternal Sharingan she got when she stole her older brother that was never mentioned before this moment's Sharingan eyes. The murderer turned out to be Deidara.Upon seeing her potential, he has informed the Akatsuki leader, who ordered him to kidnap her. She was taken into Akatsuki and treated like their own. She fled to Konoha where she was taken into the local orphanage where she met Naruto and Sasuke whom she made friends with immidietely. She was hated as a child and everyone was quite scared of her, since she had the ears and eyes of the Kyuubi. There have been several assassination attempts, but they all failed because she kept on killing the ANBU who came for her. She grew older, and graduated the Academy and became a ninja on Team 7. She loved being on the same team as her best friends, but hated Sakura ). All she did was fawn over Sasuke and was really mean to her when Kirei said that people with living parents are jerks. 'Cuz Sakura was totally a jerk after she yelled at her for saying that. With time, Orochimaru heard of her skills. He ordered the Sound Four to track her down and bring her to him. The only thing in the way was the Akatsuki, who were also after her, and the people of Konoha, who promised to defend her at all costs.
To edit since some super-talented writer cannot read a note at the top of the article.
Appearance
Aiko is often described to be quite beautiful, which is also indicated by her name and surname. Her surname was given to her by Kakashi when she refused to join neither Hyuga or Uchiha clan after they were fighting for her. (Which is completely unmentioned in her bio even though this a very important detail to her life) She has two different eyes, one containing Eternal Sharingan, while the other has SUPA Byakugan. They can mend together and create GODU MODU EYES! Stronger then Rinnengan! She is usually seen wearing a black knee-lenght kimono, tied with a red obi and normal, ankle-length ninja shoes. Many girls tend to get jealous over her incredibly petite figure and giant boobs and hips (Even though this is impossible and that she should be anorexic or fat), while she doesn't care what she eats. Ino often stalks her to see if she really doen't excercise or starve herself in order to maintain her looks.
Abilities
Aiko is able to use Sharingan and Byakugan on extremely high levels. She graduated the academy at the age of 4 and became a Chunin at the age of 5. (Yet again left out of her bio, and where? In Mizu? Didn't she graduate with Naruto's class? And genin classes only have 9 students graduate each time!) By the age of 8 she was asked to become Hokage (WHAT ABOUT MIZUKAGE?!). Most of her skills are unknown to many, due to her being trained in private and individually by Kakashi and Gai (How?). Gai mentioned at some point when she was a genin that she is above his level at Taijustu, and Kakashi's with the Sharingan. She is a genius with Byakugan, even more then Neji.
Narrator: Stares bitterly at the text and wishing for more kunai.
To edit since some super-talented writer cannot read a note at the top of the article.
For Your Amusement
Below is a kekkei genkai for your amusement--Mary-Sue of course. Instant Kill no Jutsu
Instant Kill no Jutsu will kill your opponent no matter how strong they are or what skills or defenses they have. There is absolutely no defense against this technique and it can be performed in an instant, with minimal effort, and as many times as the user wants. It can also instantly kill large groups of opponents, up to 100,000,000 at a time.
This jutsu is especially good for saving time, cutting short tedious trash talking and/or unnecessary explanations, and moving the plot forward.
With this technique, you can also enter InstaKill mode. When InstaKill mode is active, and it always is, it will automatically kill anyone who even thinks about harming you, no matter where they are. So if some dumb ninja tries be stealthy and get the jump on you by hiding in a bush, he/she will explode as soon as he/she sees you. This also doesn't require any chakra so Instant Kill no Jutsu is always active. Its even active when you are asleep.
Instant Kill no Jutsu can't be copied by Sharingan, so don't even try that bull or it will automatically kill you.
Narrator: Holding two suitcases in each hand and glaring at audience. "I hate this. I can find humor in parodies but no one has ANY idea on how terrible it is to work with Sues! They can be CRAZY! They can by STUPID! They can try to KILL ME DAILY! I barely live with some of these Crazed!Itachi wannabee chicks! My life is in danger, even more so than if I was a stuntsperson! I QUIT!"
Keira: Runs in with tears crawling down her Ivory cheeks as though they didn't want to leave her blessed cheek, but in reality they probably were struggling past the Sue-gravity-force-field to get away from her. "Narrator! Narrator please stop!"
Narrator: Twitches and scowls at her having said to the audience the above.
Keira: Sniffles, her eyes shining. "Oh Narrator! Please don't go! I'll give you anything! I know I haven't known you all of that long, but this page I was born and raised on has been fate for me! Narrator, I don't even know you're name but, I.. I.. I love you!"
Narrator: Drops suitcases in annoyance and stares at her with the classical Naruto circle eyes. "Keira..."
Keira: Eyes sparkling, saddness forgotten. Zeroing in on Narrator's face, picturing the wonderful pink, floral, and sparkling closeup on the sides of their faces as they gaze at eachother. "Narrator-sama..."
Narrator: "I am a straight woman, and even then if I was gay I wouldn't have interests in you. Plus, you don't even know my name or what I really look like. You've even been calling yourself by your clan name, misspelled at that."
Keira: Twitches and the pretty prink, floral, and sparkling scene she imagined shattered into blue and purple spiraling depression. Her eyes were replaced with the very classical Naruto circle eyes.
Both: Stare at eachother.
Keira: Sniffles, her eyes shining. "Oh Narrator! Please don't go! I'll give you anything! I know I haven't known you all of that long, but this page I was born and raised on has been fate for me! Narrator, I don't even know you're name but, you.. you.. You're my bestfriend! I love you! I want your L-pregnant baby! Please stay with me, let us get married secretly, party at gay bars, and raise our impossibly genetic children together! You'll be the dominent one, I'll be submissive!"
Narrator: Stares blankly.
Keira: Cheeks growing pink, and her eyes filling with hope. "Oh Narrator!..."
Narrator: Narrator's face grows dark like in dramatic scenes and gets Keira excited. Narrator suddenly turns to the audience and throws her left suitcase off stage infront of the front row making every audience member nearby jump. Narrator turns quickly to Keira and slams the metal part of the remaining suitcase into Keira's head.
Keira: Falls to the ground with classic Naruto circle eyes and lands face-first. Twitches on ground. Twice.
Narrator: Turns quickly and hurridly jumps off of the stage, scaring the life out of half the audience. "I'm getting out of here!" Narrator yelled frantically. Runs through middle aisle and out of the auditorium doors. The doors slam behind Narrator and light shouts of "FREEDOM! FREEHEEDOM!" can be heard.