I think drmatt's answer is a little misleading. The thing about comic books, especially Marvel comics, is that there are multiple universes, and in each universe characters can be drastically different, including how they relate to one another.

For starters, Sabretooth and John Howlett (James Howlett's father) are two different people. I feel that the answer from drmatt indicates they are the same person. John Howlett is Wolverine's father in the 'Origin' series, which came out after Wolverine had become a popular figure in the comic book world. But even then, in this origin story, there is a portion that seems to indicate that Wolverine's biological father may actually be Thomas Logan, who is Howlett's groundskeeper that ultimately kills John Howlett. In response to this, young Wolverine kills Thomas Logan (this is the scene you may have seen in the movie previews where the young Wolverine stabs a man with his claws).

There WAS a period of time in the comic universe where Sabretooth believed himself to be Wolverine's father, but this was later disproven. The identity of Sabretooth in relation to Wolverine is also still a mystery; some contend they are brothers (which is the route the movie seems to be taking), others say they were childhood friends (Sabretooth may have been known as 'Dog' in his youth).

So to answer your question: there is no concrete answer as to who his father is. It could be John Howlett or Thomas Logan. Or someone completely different. I think the writer's enjoy the ambiguity of the situation.

Here is a proper rundown of the Origin series:

http://www.typingmonkeys.com/wolverine/wolverine-the-origin/

And here is a collection of quotes and pieces of information regarding Wolverine's childhood and past:

http://www.typingmonkeys.com/wolverine/wolverine-wild-childhood/

i never knew that Wolverine's dad was ever focused in the Comic series!!!

As shown in the limited series Origin, the character known as Wolverine was born in 19th century Canada to rich plantation owners as James Howlett.

John Byrne, one of the artists, said (as stated in interviews and on his website) that he drew a possible face for Wolverine - but then learned that John Romita Sr. had already drawn one for him (Wolverine's face, drawn by Cockrum, can be seen in Uncanny X-Men #98, long before Byrne started). Later, Byrne used the drawing for Sabretooth's face (an enemy of Iron Fist, who Claremont was also currently writing). Byrne then came up with the idea of Sabretooth being Wolverine's father (they both had similar healing abilities and raging tempers).

Of course, these are comics... anything can happen...

well in my belief as i just reread origin today, that if you look closely in the panels, there is a momebnt tht rose and james see logan hanging onto something, just after the former panel shows the balcony of his mother. which is led to bleive that thomas logan is climbing down from mistress howlett's room.

this leads me to believe they are having an affair, a long running one perhaps. as it is alsso shown in one panel that elizabeth has claw marks on her side, which could either be from ehr first son john, or from thomas, but this is unclear.

it is also shown that when thomas comes to "kidnap" her, she is unsurprised or frightened. add to the fact that thoams logan look jsut like wolverine does now, makes a compelling arguement for dog (sabertooth/victor creed) to be wolverine's half brother and thomas logan his real father.

of course the other reason they made all these look alike and assumption in the comic, was to make the reveal of james's being wolverine all that more surprising, as he is nothing like wolverine, but logan and dog are.

i thin the magic of his background, is you reaolly don't know, and as long as you keep not knowing, it'll still be somehting you keep reading for and looking up, and somehting to talk about.