I'm with those who hate him for his ridiculously exaggerated powers. Overexposure is nothing new--Batman has it just as bad as Wolverine, but he still manages to entertain me no matter how often he appears. I liked Wolverine as a character because, back when he was first gaining popularity, he really was a good character. He had the bad attitude like most other "edgy" anti-heroes of the '80s (though he beat the curve by almost a decade), but he was also a really compelling character.
There were three things I loved about Wolverine: 1) the scrappy underdog aspect, 2) the man out of time because he lost his past, and 3) the would-be samurai constantly struggling to cage the savage beast inside himself. Gradually, however, Marvel has stripped away those elements. First went the underdog aspect when his healing factor gained power to the point that he can be blown up, shot full of holes, have his face torn off, lose a significant portion of body mass, etc. and still keep fighting like nothing's wrong. A character who's an invincible tank going up against the likes of street thugs and ninjas does not an interesting conflict make. Next went the struggle between discipline and savagery when he just started giving into his savage side, killing people without remorse and happily ditching his years of training to fight like a drunken brawler while leaning on the aforementioned exaggerated healing factor. All Marvel's got left now is the man of mystery aspect, which they're exploring by finally giving Wolverine his memories back. Unfortunately, that's tainted by everything else the character's already lost. I appreciate that Marvel's exploring Wolverine's past with Origins, but I can't get invested in any kind of Wolverine story anymore to see how it goes because his character's just not interesting on other levels.