Short answer: The Wolverine is an adequate superhero movie, but you've almost certainly seen this story before, even if you haven't read the exact comics this movie is based on.
Spoilers ahead, by the way.
I've never been that much of a Wolverine fan. When I was collecting comic books, I had a different first choice for my stories about a tough, cyncial, flawed hero. I was disappointed when the first three X-Men movies basically turned out to be "Wolverine and His Less Competent Friends". So it may not be much of a surprise that I thought this particular outing for the super-healing Aussie was lukewarm at best.
But the basic story of The Wolverine is completely paint-by-the-numbers. You start with your hard-edged hero, who's suffering from a painful past and hiding his bad-assitude under a basket. Then he's offered a chance to do something meaningful and noble. He tries to walk away, but eventually finds that he can't; he's become smitten with the story's damsel in distress, who is sufficiently helpless that the hero must come to her rescue. He succeeds, and by doing so, he rediscovers himself and his purpose.
The movie just keeps hitting the same old cliches, right down to the love-em-and-leave-em, "I don't fit into your world, babe" ending. I know that some of this story actually predates the movie, although there's not much in common between the original comics and the movie aside from a few characters and the general theme. With so much divergence from the source material, the scriptwriters certainly could have invented a less cliche Wolverine/Mariko storyline.
There are a few good moments in the movie, and Yukio is a fun character I wouldn't mind seeing more of. And, of course, there's the mid-credits teaser for the next movie, which by itself will probably justify the price of admission for hardcore fans. If you're keen to see Hugh Jackman beat up ninja or take his shirt off a lot, you're well-served by The Wolverine, but otherwise, there's nothing special or noteworthy here.