To preface this discussion, I do consider myself a fan of X-Men. I've never been a comic book reader, but I've seen all of the movies, followed a few of the different TV incarnations since the early '90s, and played through some of the video games (particularly X-Men Legends and its sequel). That being said, although I don't qualify as what some would consider a true fan or hardcore fan due to my lack of exposure to the original source material, I feel that I have a fair grasp of the X-Men universe and a decent knowledge of its characters. And also for the record, I enjoyed the first five films and even thought the first three held up pretty well when I rewatched them in the days leading up to seeing The Wolverine.
All I knew about The Wolverine in advance was that it focused on Logan and that it took place after X-Men: The Last Stand. I didn't see a single trailer beforehand, and I had no idea which actors to expect other than Hugh Jackman. I went into the theater without expectations of any kind and yet I was disappointed, mainly because of what I didn't see in this latest franchise installment.
The title's lack of the franchise name "X-Men" is appropriate because with the exception of a few dreams/flashbacks/telekinetic instances with Jean Grey, there aren't any mutants other than Wolverine you've seen in the previous films and most likely none that you've even heard of. Instead there's a story set in Japan with a Samurai or Yakuza family obsessed with Wolverine's powers and a villain that's general to the Marvel universe and possibly more tied in with Captain America and The Avengers than the X-Men. After a bit of research, I discovered that The Wolverine is based on the similarly titled Wolverine comic series which began in the early '80s. In following this particular storyline, the film probably does a great job (and I think the current consensus among hardcore fans is that it does), but for the more casual X-Men fan like myself this movie was hard to enjoy because the characters were unfamiliar and frankly boring in comparison to the 30+ mutants I already know and love. It's not a bad movie by any means; it's just incredibly far removed from what most people know of the X-Men universe. The character development seen in Logan is solid yet marginal considering the emphasis the first four films already put on him, but Hugh Jackman delivers perfectly as always.
If you like X-Men (particularly Jackman's Wolverine) or simply action movies in Japanese settings, I recommend seeing The Wolverine eventually even if that means waiting for a rental. If neither of the above applies to you, this one is a very skippable movie, and for the record I wouldn't recommend this as a first exposure to X-Men (instead try X-Men  or X-Men: First Class ). Whenever you watch this movie though, be sure to wait for the short teaser scene after the end of the credits. This scene alone elicited more excitement from the theater than the entirety of the actual film on the ticket stub, indicative of the fact that there's a world full of casual comic fans who don't actually read the comics and that we are beyond stoked to see X-Men: Days of Future Past next year!