Character Development
By the start of the 21st Century, Marvel wished to expand Wolverine's back-story and this was released. Many were upset by its content of a young Jimmy, as a "whiny, rich kid". I agree that this was a slow built origin but then wasn't that the point? This is for those who wish to know who Marvel choose to develop the character, and is also where they mined most of the opening for X-Men Origins: Wolverine.
Wolverine: Origin - Paul Jenkins and Adam Kubert
This mini-series was put out by Marvel to tell the story of Wolverine's youth, way before Weapon X and all the way back to the 19th Century...with the mini-series, Wolverine: Origin.
*Spoilers* Origin revealed that Wolverine's real name is James Howlett, the son of a wealthy Canadian landowner in the late 19th Century. He was the illegitimate son of his mother and their groundskeeper (called Logan). Little Jimmy was a very sickly child; it wasn't until one night when his father Logan shot John Howlett did his powers manifest. These powers drove James into a berserker rage leading him to murder Logan and accidently his mother. He also stabbed his childhood friend, rose, in much the same way. This trauma caused James to become Wolverine, a feral beast who lives in the wilderness. He apparently suppressed all of this thanks to his healing factor...right, I dislike that part of this run. This is a mixed bag, if you are a fan and want to know more then get this. If not, then skip it and play the game, Origins: Wolverine.
Wolverine: Enemy of the State - Mark Millar and John Romita, Jr.
This is literally Wolverine vs. Everyone in the Marvel Universe. After severe brainwashing, Wolverine goes on a hunt of his former friends and chaos ensues. Enemy of the State saw Gorgon, then-current leader of the Hand, form an alliance with Hydra forces, go on a rampage of murdering superheroes and resurrecting them as brainwashed servants. This story arc saw Wolverine die, because he actually can die, and become the figure this cabal needed to attack the best of the Marvel universe. For those who don't know, you can kill Wolverine if you strike Logan with a quick decapitation and keep his head far from its body. Enemy of the State is the ultra action Wolverine story; he is forced to attack his friends in the Fantastic Four and X-Men and kills a bunch of S.H.I.E.L.D. agents. It is only after he was finally captured and regained control of his mind after a lengthy, painful deprogramming session. Does he wage an all-out war against Hand/Hydra. An interesting knock on effect to his story is that it lead to Wolverine becoming an Avenger due to the damage to his reputation after killing a lot of people. Captain America makes him a part of the New Avengers team. It is dumb but very, very fun.
Honourable Mentions: Wolverine: Old Man Logan by Mark Millar and Steve McNiven and Uncanny X-Men #251.