As I think others have mentioned, Eve tends to make it a bit tricky in that capsuleers are, by default, not an average citizen. Unfathomable power and wealth, etc means that a number of the metrics you might use to judge a character in another game, or the protagonist in your Twilight fan fic, don't apply. Other metrics though, I think, do still apply.
I don't think I've got a lot of Mary Sue type stuff with Silver, in particular. He is largely a product of the character creator, and although his story has at times gotten a bit exotic I think most of it developed in a pretty natural way. Medical training
and being a pilot might have been stretching it, but then again being a pilot is how he segued into being a capsuleer and he's had a long time since then with fancy implants and essentially unlimited resources to pursue his interests in the medical field. Plus there was the whole Happy Chip thing and I needed him to have a bit of a useful background for that.
Also, I try and make sure that if my characters are very good at some things, they are terrible at others. Silver is great at press releases and pretty good on rhetoric, but fairly terrible at relating to anyone on a personal level. He would also get his ass kicked in person by almost anyone, can't really hold his liquor, and has a sense of style that runs to suits and other suits that are just a slightly different color.
Hilion rather intentionally hits some Mary Sue tropes. He was intended from the start as a bit over the top. He's over 100 years old, he's constantly practicing substance abuse (well, I say practicing, but he's really an expert by now), he has a weird and rather variable accent, he's an unusual height, etc. On the other hand, I think he is lacking an important Mary Sue ingredient, which is that noone is expected to take him very seriously. He will tell you, with a straight face, that he once escaped the clutches of a hyperintelligent Fedo the size of a VW Beetle and that there is a planet where he is worshiped as a deity and that he is a Brutor (in spite of being a very short Khanid).
One thing I think has been mentioned that is cool in Eve is that you don't need to make up a crazy story for your character to be a special snowflake - you can sometimes have the opportunity to do it through the game. You can
actually be an expert if corp infiltration, or have your own industrial empire. Some of us have also had the opportunity to participate in big events or bits of Eve history whether player or CCP generated.