I just don't get all the Wolverine hate in here. Ok, he's overexposed. Hell, one could argue ANY major Marvel character has been overexposed at one point in their existence or another. Honestly, I think that (as good as he is), Spider-Man is overexposed.
Wolverine was a significant advance in the evolution of Marvel characters: a prototype anti-hero. A "dangerous good guy". I remember something that one of his creators said (this is from memory, so it's not 100% but close):
Wolverine is a character that you're glad he's on your side because you DON'T want to be on the other side of. He's also very volatile. Kitty Pryde could walk into the kitchen to find Wolverine reading the newspaper and accidently say or do the wrong thing. Cyclops would then come running to see what the disturbance was and find the kitchen plastered with "Kitty bits" and Wolverine back to calmly reading the newspaper.
He was (and is) a vital balancing character for the X-Men. Pragmatist to their idealistism. Rationalist to their emotional compassion. And yes, the "enforcer" that ANY cause has hidden away somewhere or another, acknowledged or not. The man who does the "hard things" that the others either cannot bring themselves to do, or cannot afford to be SEEN doing.
The Scott/Jean/Logan triangle was always interesting because for Jean Logan represented her wild side, her inner passion (esp when she's a Phoenix host) that "Stick up his a** Summers" could never accept, let alone be.