Here's a review by one of the Gawker websites, which gives a pretty accurate view of the movie
We see Wolverine as a kid, with his brother, and something terrible happens and Logan's mutant power is revealed.
Then flash forward: it's the 1970s in Vietnam, and Logan and his "brother" Victor (Sabretooth) are soldiers. Victor has been going psycho and killing anyone who looks at him crosswise, so both mutants wind up locked in the brig. Until Stryker, a high-ranking officer, comes and tells them he's putting together a special team, with special privileges.
The elite special-ops team is made up of mutants with cool powers. One of the members of the team is the sword-wielding Wade Wilson, aka Deadpool, who keeps making dumb jokes and driving everybody else nuts. Everybody keeps telling Wade to shut up, and Victor nearly kills Wade until Logan intervenes. The team takes on tons of missions, with Victor getting more and more bloodthirsty.
But Logan draws the line at having to kill innocent people, and walks away. He lives in a cabin in the woods, becoming a lumberjack (and he's okay), with his girlfriend Silver Fox. Meanwhile, someone is killing all the members of that special-ops team one by one. (The first to die is Beak, who uses electricity.) Stryker comes to warn Wolverine, but he says he can take care of himself... right before he finds Silver Fox with her throat cut.
This time it's personal. Wolverine goes after Victor, and they fight, but their powers are too evenly matched. So Wolverine goes back to Stryker and lets the military officer put him in a goo bath, giving him new adamantium skeleton and blades. And we find out where the name "Wolverine" comes from.
And in the end, we find out Stryker is kidnapping mutants and keeping them prisoner so he can harvest their DNA. All of these mutants are being held prisoner on an island, which turns out to be the Three Mile Island. It turns out Stryker has been harvesting mutant DNA to breed one super-mutant, who will have all the superpowers of the other mutants... and that mutant is Wade Wilson, aka Deadpool. Stryker doesn't want to release the super-mutant because he's not ready yet, but the nearly indestructible Wolverine is tearing everything up.
So finally Stryker releases Deadpool, who now is bald with flame shooting out of his sunken red eyes, and the ability to disappear like Wraith. And Deadpool's mouth is sewn shut, causing Wolverine to quip, "They finally shut you up." And Deadpool's trusty sword comes out of his fist — just like Wolverine's claws. The fight moves to the top of one of the nuclear reactors, and Deadpool is shooting everything with his eye-blasts, destroying all the reactors.
Wolverine almost falls into the reactor, but an arm reaches out and saves him — and it's Sabretooth. Who says, "Nobody kills you but me, brother." Then Sabretooth says "Back to back," and the two mutants fight back to back, so they can see on both sides. Wolverine slices Deadpool's head off with one swipe. Says Sabretooth, "You know, this doesn't mean we're not still enemies," and then he takes off.
And then — here's my favorite part — Wolverine is freeing all the mutant captives. And Stryker says he has a "magic bullet" to shoot Logan with. The other scientists point out that it won't kill Logan. Stryker says, "I know, but if I shoot him in the head, it'll erase his memory." So he shoots Logan in the head, and he falls to the ground, apparently dead. But then he wakes up with total amnesia. Gambit drags Logan to safety and says he's a friend. Then we hear Patrick Stewart's voice (as Professor X) telling the escaping mutants to come to him, and he'll keep them safe. [We Are Movie Geeks via Worst Previews]