I find lot of Mary-Sues to have very strong, tough personalities. They tend to be snarky, confident either when they need to or all the time, and unbreakable. What I mean is they are unnecessarily badass.
Now, tell me if this sounds familiar. 'They're tough but once you get to know them, they're friendly. If anyone insults their friends or family, they'll attack.' That was poorly written but you readers must know what I'm taking about. The go-to personality.
This type of character is great when written well but most the time they aren't. Characters start out too strong in both areas so no character development can take place. Katniss Everdeen is a great example of when a character is given this personality and has been written well. But I'm sure we all could name at least one character who wasn't. I bet they where close to being, if not, a Mary-Sue.
I personally see this most frequently in RP characters and with anyone with geeking will know. (It's an app).
I'm just bored of every main character being unnecessarily rebellious or whatever. Seriously, when a main character is made to cover the tough and friendly bases all at once, it's really hard to see them as anything but Mary-Sue.
My advice would be to start out with a character that, through development, grows more or less badass/rebellious.
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Anti Mary-Sue Character Guide
Non-FictionHere is just my list of tips of how to avoid creating/writing a Mary-Sue character. Take them as you wish. Greatest Achievements: #1 in non-fiction!!!