Being such a comic book nerd, I'd be the first to say that when it comes to super-hero titles, "team books" and "solo books" do have a different rythm to them. If handled properly any writer can make a solo character suddenly fit into the structure of a team and on the flip-side they could explore what a character that's normally part of a team does when they aren't surrounded by their peers. Wolverine is a character that does lend himself so well to both types of stories. He's fun to watch as the violent and scrappy ass-kicker of the X-Men, but he is also tortured and conflicted enough to take out his rage on those deserving all by himself. Bryan Singer and co. certainly captured the spirit of Logan very well when they introduced him as the lead character of the X-Men movie. He can't remember his past, but he can heal from any injury and due to experimentation he has a razor sharp steel alloy grafted to his skeleton (the fictional element of adamantium).
Visually there is a lot to play with, but it also makes for an interesting psychology for an actor to delve into. If one looks at Hugh Jackman's filmography, there really isn't much before the first X-Men film. He is now an accomplished actor with excellent performances in such films as The Prestige and Les Miserables, but I'd argue that no matter what else may come, Wolverine will probably be the role he is most remembered for. His take on the character is iconic to the point where I can't imagine anyone else playing him. Batman and Superman and Spider-Man have all had other incarnations, but a non-Hugh Jackman Wolverine is pretty hard to conjure up any imagery. His embodyment of the role is just as recognizable as say Clint Eastwood as the Man with No Name.
Unfortunately, I've felt that the majority of the X-Men films have been lacking in story and character. Singer certinaly cracked the code to a successful comic-book adaptation of the franchise similar to Sam Raimi with Spider-Man, but I've just come to love and enjoy what the genre had later turned into with works such as The Dark Knight or The Avengers. I actually think Matthew Vaughn told the best on-screen X-Men tale with First Class, but James Mangold's The Wolverine, despite a few flaws, can certainly sit right below the prequel film (First Class, not Origins I mean) in a ranking.
Mangold is an extremely talented director with a vast range of films (Heavy, Cop Land, Girl Interrupted, Identity, Walk the Line, and 3:10 to Yuma are some of my favorites of his). Similar to Curtis Hanson, he can really tell a variety of stories, but sometimes the screenplay he works off of might not be as fully developed, unique, or complex as one might hope (Knight and Day comes to mind). The Wolverine (based in parts on the Chris Claremont and Frank Miller 1980s miniseries) is smart in how it moves from a Japanese-set mystery to a stylized samurai action film. It features the most character development that Wolverine has seen in the past four to five films and thanks to Jackman - and supporting turns by newer actresses Tao Okamoto and Rila Fukushima as Logan's personal and professional partners (who hold their own against Jackman's presence) - the film has a gusto to it that's only hampered by some senseless twists and turns during the third act. Still, the odd and ultimately impersonal twist doesn't take much away from the film's enjoyment (a sequence aboard a bullet train is particularly gratifying) and this is the most fearsome and vulnerable audiences will see Wolverine... at least until the next film. I just wish it didn't take five movies to get to this interesting of a point.