Having read a couple dozen of Marvel's "Essential" series, I've seen the gamut from excellent to awful. Generally, what makes the comics good are exactly the things you'd expect: good, consistent writing and art, strong characters and a decent supporting cast. (This last feature seems to often be the deciding factor for excellence: it's a reason the Essential Spiderman volumes have been exceptional, while the Silver Surfer was not on the same par.) By these standards, the Essential Wolverine is a top-notch book.
Wolverine is, of course, one of the X-Men, but there came a certain point when he became something more than that. I personally feel that he emerged from being a rather one-dimensional character back in the early `80s during the early issues of the "New" X-Men. In particular, during a storyline around issue 130, the rest of the team had been defeated by a band of villains known as the Hellfire Club, but Wolverine, a character who seemed to be the least powerful, came back to rescue his teammates. He did so in a violent manner, with little qualms about killing or maiming, making him a distinct contrast to many other heroes. Later, Frank Miller gave Wolverine even more of an edge in a mini-series and added the first person narration that was rare at the time but is now commonly associated with this superhero.
Not all team characters can stand on their own in their own book, but, as this book shows, Wolverine can. It helps that this volume features a roster of Marvel all-stars: Chris Claremont, John Byrne, Peter David, John Buscema, Archie Goodwin and Klaus Janson (no third-stringers in this bunch). The stories start off during a period when the X-Men had faked their own deaths, and Wolverine goes off to the fictional principality of Madripoor, an East Asian city-state somewhat akin to Singapore. It also bears more than a passing resemblance to the Casablanca of movie fame, a city filled with various lowlifes and people seeking refuge from other places.
Wolverine has a connection with Madripoor going back years and feels quite comfortable in this seedy town. He adopts an alias of Patch (which fools less people than he thinks) and gets involved in various capers, starting with the theft of an evil sword. This introduces some of the major supporting characters, particularly Jessica Drew (the former Spiderwoman turned private eye) and her partner, ex-actress Lindsay McCabe. This caper also gets Wolverine tangled up with old enemy Silver Samurai, but not in a fully adversarial way.
Other stories get more characters introduced, particularly the various crime lords of Madripoor and the coldly pragmatic Prince. Probably the most interesting foe in this volume is Roughhouse who starts off as a simple tough guy villain but develops into someone far more interesting by the final issue. Most of the stories span over several issues, with the last two taking six and seven issues respectively.
As stated earlier, the Essentials volumes vary in quality, but this book is one of the best. With great characters and storytelling, this volume easily rates five stars and, if you enjoy comic books, this is one really fits the definition of "essential."