I'm a character designer who enjoys creating and writing comic books. So what I think makes a videgame character design great and that stands the test of time is because of the simplicity in design....and having a popular game helps, of course. :)
But what makes a character an "icon" as opposed to just being "popular?"
Mario, Link, and Samus are so iconic because their easily recognizable, have only a few major colors, plus they're also "cool" looking. (yes, even Mario :D ) So they're simple, yet, brilliant in design. Like they say, "Less is more." I think the perfect example of a game with the most memorable cast was Street Fighter 2 including Cammy. ALL of those characters are brilliantly designed and are iconic even till' today.
I counteract my views by pointing out RPG characters. Lately they've been looking complex and are designed with too much detail. For example, like the characters from the newer Square-Enix games. Since FF7, most of their character designs are now looking more complex and they all tend to look the same. No matter how popular a game is, if the characters are too complex and crazy looking, I don't think it will become an icon like the characters that we all know and love.
(OTHER ICONS INCLUDE: Solid Snake, Cloud Strife, Master Chief, a bundle of others, AND OF COURSE....Pac-Man! )