Wolverine -  

Probably one of the oldest X-men around, while not a member of the original X-men, there have been flashbacks of him in World War II and prior, long before the adamantium plating.  His regenaration abilities, short of decaptitation, make him immortal.  

The idea of Wolverine though has pretty much been standard issue for the past several generations of comics.  He was a member of the Weapon X program (Canadian Mutants) and was chosen for the proess of admantium plating (along with Sabertooth), but he wrecks the lab after a successful operation shutting it Alkalie (sp) Island down for several years.  Until Deathstrike then later Experiment 23 (lore for both is kinda hit or miss) have similar operations down the line.   

As much as X-men Origins is a terrible movie, they got this right.  Wolverine's origins are pretty much unchanged and probably one of the weaker backstories of all the X-men.

It's kinda hard to say what's the right backstory for any established character in the Marvel or DC universe. If you aren't familiar with comic books there's this fun concept of continuity that usually gets beaten, bashed and turned on its head every now and again. Basically once a storyline has gone on for a set period of time the editors deem the story too convoluted for a new audience, they scrap the world entirely or kill off most of the cast, and start fresh. Wolverine is one of the most popular Marvel characters, hence he's been done 100 different ways by 100 different authors, so his backstory and personality can change depending on who writes him, as well as the roles and personalities of supporting characters.

In essense the character is always the same, he's a tough guy but not a complete asshole, his mutant powers give him ferral tendancies and abilities which sometimes come at odds with his humanity. His powers are usually the same also, a healing factor that basically lets him regenerate from any wound and keeps him relatively young, bone claws with nigh indestructable adamantium bonded to them, and ferral senses of hearing and smell. His backstory there's a bit more play with, he's usually born late 19th century to early 20th century as James Howlett, sometimes he's raised in a Native American Blackfoot tribe, sometimes he moves to Japan and marries a Japanese woman, in general he's fairly worldly and can be fluent in several languages. At some point he gets captured and forced into the Weapon X program by those damn Canadian warmongers which seeks to alter or create mutants for living weapons. This always leads to 2 things, the adamantium being bonded to his skeleton and amnesia which fosters his mysterious past. Shit happens, he joins the X-men, etc.

Characters like Sabertooth have had different origins as well depending on what run of the series you read, he can be a complete stranger, Wolverine's brother, son or even father though I don't know if the father origin was just a concept or if it was ever published. In general Sabertooth always acts as Wolverine's rival and a bad guy with similar powers to Wolverine and an inferiority complex.

Wolverine's love interests tend to get killed off, though he does have flings with other female mutants here and there.

So in terms of accuracy it's a reasonable backstory and didn't completely miss the mark, got most of the important bits in. It fucked over Deadpool though, if you read into his backstory it's usually pretty twisted and puts a lot more weight behind the Deadpool name. With the release of X-Men: First Class the director basically stated he was ignoring X-Men: Last Stand and Wolverine: Origins from the continuity of the series, but it's still a decent primer for Wolverine if you aren't into comics.

The two stories that deal with major key elements from Wolverine's most-recognized origin are Weapon X, and the...very-originally named...Origin. Yeah, I'll bet they spent weeks thinking of that title...Neither story tell the complete backstory of Wolverine, of course, but again, they're major elements. The Wolverine movie had elements from both stories incorporated in it; just....not very well, unfortunately. There was a lot of potential for this movie that was sadly wasted. I think that overall, taking the movie for what it is, it was okay, but again, they wasted a lot of potential. I think you more or less watch the movie for Hugh Jackman. He's great.

As Yawaru discusses a bit, details of his backstory have always been ambiguous, or have out-and-out changed completely, and/or were retconned terribly. At one point, Wolverine was the decendant of.....wolf people...or something. Seriously. I don't think Marvel has gone with that explanation lately though....

The movie makes it seem like Wolverine and Sabretooth were brothers, which...is something that never happened in the funnybooks. Sabretooth has claimed to be Wolverine's father, I think (as Yawaru mentioned), but that proved to not be the case, either. I'm not sure, in the movie, if they are supposed to be literal brothers, or metaphorically. That was also kind of ambiguous.

I also didn't appreciate what they did with Deadpool in this movie either...Although he was also a product of Weapon X....it wasn't that!! Yeesh...Just another waste...

So after reading the above I will remove the back story as a dislike about the movie but will still say the movie sucks.

...Probably a good idea. ;P I'd definitely check out both Weapon X and Origin, if you're interested in Wolverine's...uh, origin. Although, again, I thought that, taking the movie for what it is, it was...okay. Hugh Jackman is what really sells it. He's great. If not for him, it...would have been worse, for me, anyway.

It sounds like they also plan to make the second Wolverine movie (yes, there will be another. Despite bad reviews, it did make mad cash) about the critically-acclaimed story by Chris Claremont and Frank Miller, where Wolverine goes to Japan, and gets married, which Yawaru also mentioned. So. You might want to read that, too! But again, it's regarded as a great Wolverine story, too, so...