- Mary Sues are all self-insertions/all self-insertions are Mary Sues
Not all Mary Sues are self-insertions and not all self-insertions are Mary Sues. A Mary Sue can be vastly different from the author, yet still be an "author's darling." Toula from My Big Fat Greek Wedding was very much a self-insertion, yet one would be hard-pressed to label her a Mary Sue. Even Luke Skywalker (George Lucas, anyone?) was portrayed as enough of a naive dweeb that he managed to get by without tripping the Sue-dar.
- Mary Sues are characters that are cliched/unoriginal.
Not all cliched characters are Mary Sues, and not all Mary Sues are cliched characters.
If this myth were true, then every stock character (cliches at their purest) would be a Mary Sue. It would be quite a stretch indeed to call the greedy merchant who appears in one chapter a Mary Sue, or to apply the label to the stuffy librarian in coke-bottle glasses. These archetypes may not be original, but they're most certainly not Mary Sues.
Some Sues are quite original, but their originality is either outweighed by or is part of their Sueness. Consider Nancy Drew, the first girl detective. She's beautiful, smart, has an incredibly hot boyfriend, and anyone who doesn't like her is a rotten scoundrel and/or with the bad guys. And then there's James Bond, the womanizing super-spy.
- My friends, family, and/or some other people say my character isn't a Mary Sue, so I know it isn't.
Asking your friends and family to review your work is a good start, but it's not necessarily enough. It can be very difficult to get objective, unbiased opinions from your friends and family. The more opinions, the better. Get them from older people and from people who have read more literature. Get opinions from people who aren't afraid to tell you how bad your story is if they don't like it. You may not like what you hear, but it will be well worth it.
Also, what are your reviewers into? Do they consider cartoons like Naruto and InuYasha to be the best thing in anime ever? Do they think that books like Eragon and Twilight are the greatest literary acheivements since Lord of the Rings and Dracula? If so, get a second (and third, fourth, fifth, etc.) opinion fast.
- Mary Sues are always flawless/my character has flaws, so she can't be a Sue.
Not true; many Mary Sues have what one would consider character flaws, but they are handled very badly. The flaws of a Mary Sue are often romanticized and/or clumsily used to make the reader sympathic to the character. They also may work out to the Sue's advantage. (EG, the romantic lead finds a trait that Mary's schoolmates teased her about her entire life endearing.) Flaws can and do make a character more likable; the Mary Sue just uses the wrong ones in the wrong ways.
- It's possible to write a Mary Sue well, so it'll be okay if I proceed with mine.
Maybe, and that's a huge maybe if you're not very experienced. It won't hurt you to try, but unless you're very experienced with handling characters chances are good that it won't work. That said, you can try. It won't hurt. Just make sure that you ask for opinions from people who aren't afraid to give them.
- Any character with an unusual or exotic trait is a Mary Sue.
This just isn't true. Unusual traits can be used without any problem, so long as they are used in a way that does not feel ostentatious or superflouous. However, many naive writers use them as a gimmick to make their character stand out and appear unique from everyone else.
- Characters in old stories and ancient legends were always perfect; perfection is just part of heroic epics.
Hardly! Flawed characters have been around since the earliest known literature. Stories of mighty Thor show that for all his great strength he wasn't too bright. Gilgamesh, the oldest epic hero known to mankind, was also a bit thick-headed. King Arthur made a whopper that lead to his death.
The original Aladdin was a lazy bum who just got lucky. Little Red Riding Hood ended up in a pickle because of her naivety and failure to listen to her mother's warnings. The princess in the Frog Prince story is a selfish brat who only gets her prince after she attempts to kill the frog. Characters such as Nasreddin Hodja and Haroun al-Rashid were portrayed as clever, but not infallable.
- I've written fanfiction/been roleplaying for years, so I have experience.
This isn't quite a Mary Sue myth, but it still needs addressed. Besides practice, you need to study. You have to get out and find out what people like and don't like. You have to learn what entails good and bad writing. You have to read other authors to get a feel for how well-written stories are told.
Think of it like trying to practice a sport knowing only half the rules: you can practice for the rest of your life with what you know, but you'll never learn the rest of the rules, and thus you'll never know what you're doing wrong. The same goes for writing: unless you learn the rules, you won't know where you're going wrong.