The possibility of doing a "brief" history of Wolverine gets more and more remote the longer he's around. Not because each year brings all new adventures for the character - that, you'd expect - but because more and more details keep being "revealed" about his past, and with each new detail, comes new levels of ridiculousness. Nonetheless, here's what you really need to know about the character:
Wolverine was born James Howlett (Yes, really) in 19th century Canada to John and Elizabeth Howlett, plantation owners, although it's strongly hinted that his father is actually Thomas Logan, who works on the Howlett family plantation and had had an affair with Elizabeth prior to James' birth. It's also been strongly hinted that whoever James' father is, he's descended from evolved canines, much in the same way that regular humans are descended from evolved apes.
Don't worry. It gets better. Well, kind of.
When James is an adolescent, John Howlett is killed in front of him by Logan, prompting James to pop his claws for the first time and go into the first of many berserker rages, killing Logan and injuring Logan's son, "Dog"... who, in yet another strong hinting, just may be future nemesis Sabretooth. Going on the run following this - even though he can't remember it, due to his healing factor placing a mental block on him to protect him from the truth (No, really, I'm not making this up) - he adopts the name Logan and ends up accidentally killing the woman he loves in the middle of a battle with Dog, who now looks just like Sabretooth, before a new mental block makes him forget that as well.
Yes, we've only just started with the running themes.
After accidentally slaughtering an entire town due to another berserker rage following another true love dying (this time actually murdered by Sabretooth, as opposed to Logan himself), Logan realizes that there's only one place for such a mentally unstable killing machine, and enlists in the military. Luckily, he meets a girl, falls in love and she gets killed. Cue another berserker rage. This pattern continues while Logan works his way through the Canadian military, a stint in Russia learning to be a spy, fighting with American soldiers in WWII, and also joining in the Spanish Civil War for a bit. Say what you like about those berserker rages, but they apparently pay well in terms of air miles.
Post WWII, Logan travels to China and Japan, where he tries to find some semblance of peace of mind, and instead only succeeds in finding ninjas and evil demons who cause (a) Logan to accidentally kill someone with his claws, and (b) another true love to be killed. But wait! This latest true love is also the mother of Logan's first child (that we know about), so she's a little bit more important than the rest. Anyway, bored with all the death, Logan joins the CIA, which turns out to be a very bad idea indeed.
By this point, Logan's memory is a bit of a mess; his healing factor keeps sealing off traumatic memories, and given that he keeps finding true loves murdered and/or accidentally killing people, there are rather a lot of those. The CIA, having realized this, decide to help out, and give him false memory implants that also just happen to help them control him that little bit better. Of course, the inevitable happens - Innocents die (killed by Sabretooth again, with the express purpose of messing with Logan's head) and Logan quits, deciding that American secret services suck and that he'd rather work for the Canadian Department of National Defense.
It doesn't last long; before too long, he's kidnapped by the Weapon X Program - And this is the point where you're going "Thank God we're finally getting to a point I remember" - where he gets adamantium coatings on his bones that also happens to drive him into a (Yup, you guessed it) berserker rage that ends with him killing lots of people and disappearing into the woods a complete amnesiac.
It's in those same woods - You know, the generic Canadian ones - where he's discovered by James Hudson, later the leader of Canadian superhero team Alpha Flight, and nursed back to something resembling sanity before going to work for the Canadian government's Department H program, which worked around the clock to create superheroes who said "eh" at the end of each sentence. It clearly wasn't fulfilling work, however; as soon as Professor Xavier visited to invite him to join the X-Men, he was slicing ties and on the first jet to America. After that, the rest is history.
...Or, actually, not exactly. For one thing, Wolverine has died repeatedly since joining the X-Men, and been reborn each time through a series of unlikely plot developments; this turns out to be because, each time he died, he ended up fighting an angel in the afterlife and being resurrected. Because, you know, that's what you do when you die. He's also had all the adamantium stripped from his bones (and then reinserted), regained all of his memories as a side-effect of a trip to an alternate reality, and met his son (Now Dark Wolverine from the Dark Avengers) and his daughter, who's really a teenage female clone of him. In amongst all of this, he has, thankfully, managed to stop accidentally killing people, although he does still have a bit of a problem with the women he loves ending up dead. Oh, but there is one piece of payback: He did manage to kill Sabretooth, after discovering that he might be part-canine on his father's side. Or something.
Admit it; now you wish that you had a healing factor that would block all of that from your memory.