The Wolverine is pretty darn good. Especially when compared with the train wreck that was X-Men Origins: Wolverine from 2009. I had forgotten how truly awful that film was until I re-watched it on TV the other day. Yikes.
I will admit, I am not a regular reader of Marvel Comics. I was a DC girl growing up (Batman and Wonder Woman 4eva!). But I am aware of the X-Men mythos, have many friends who have filled me in on the various story lines, and have seen all of the X-Men related films.
Hugh Jackman makes Wolverine a compelling antihero, and he's just as good in this film as he has been in all five previous films (X-Men, X2: X-Men United, X-Men: The Last Stand, X-Men Origins: Wolverine, X-Men: First Class). He appears to me to have bulked up extra big for this film - when he gets his inner animal riled up he's physically very formidable.
This film is the story of how he meets Mariko, the love of his life, and introduces various characters well known from the comics such as Yukio, Madame Hydra/Viper, and the Silver Samurai. There's the usual amount of big action sequences (which run a bit too long for my tastes) balanced out with a nice amount of emotion-focused character development for Logan along the way. Logan is without his mutant healing abilities for much of the film, and this allows for a re-focus from Logan's physical to his emotional side consistent with the story being told.
Is the Silver Samurai's story the same one as from the comics? No. Is Logan meeting Mariko after he's already loved and lost Jean Grey? Yes. Can we overlook these continuity differences from the comics? Depends on who you are, I guess. Since I wasn't already a huge fan of the franchise from the comics, I can easily accept these changes and enjoy the story that is told.
Oh, and make sure you stay through the credits. There's a nice hook into the upcoming X-Men: Days of Future Past film coming out next year.