It's tough to say. Once I rolled up a character with three 18s (I had witnesses), but the campaign never got off the ground.
I remember back in middle school being all gaga over the Heroes of the Lance in... wouldn't it be awesome to play Raistlin? And go through those Dragonlance modules? But on second thought, I think I did play Raistlin, and we started the first module, but didn't get very far. The DM didn't like how it deviated from the book... ha!
I've never played a character going from 1st level to 20th level (or whatever's considered the highest level in a given edition), in all the years I've been playing D&D. I think it'd be pretty cool to do that. But most campaigns just don't last that long.