http://tvtropes.org/pmwiki/pmwiki.php/Main/FurAgainstFang
http://tvtropes.org/pmwiki/pmwiki.php/Main/NewerThanTheyThink
Most "real-life" legends and folklore mention little or nothing about any animosity between these two supernaturals. The myths most commonly thought of when you hear those terms, from Eastern Europe, actually mostly state that either werewolves become vampires when they're killed and not properly disposed of, or that the two creatures are the same thing.
Probably the first movie source for a conflict between a werewolf and vampire is Dracula vs. The Wolfman. That was simply because you had these two awesome supernatural creatures and wanted to see who'd win; pure pulp fiction. It wasn't until later that the whole "Fur vs Fang" thing was fleshed out by novelists and screenwriters to provide more of a historical source for the feud. Obviously the only similarity between most of the more popular backstories is that they don't much like each other:
Underworld has the two races sharing a common ancestor, with the wolf ancestor being an uncontrollable monster that most of the vampire race were created specifically to counter. The wolves were then enslaved by the vampires, which eventually fostered a hatred among werewolves that led to the war. Both perpetuate the species by "infecting" humans with a virus, and apparently it takes a pretty strong human to survive the ordeal and "twist" the virus's effects to gain immortality.
Harry Potter mentions that vampires and werewolves exist, but doesn't go very deeply into their backstories and mentions no racial animosity; the only vampire I remember from HP is pretty much comic relief in one of Slughorn's parties. The werewolves are covered more, as Lupin, a prominent backstory and supporting character, is one, and the affliction is considered a disease that is incurable but manageable.
In Twilight the Quileute "werewolves" are actually more "shape-shifters" that came upon the ability genetically, completely independent of their encountering vampires. The hatred is mostly on the part of the werewolves towards the vampires due to their first encounter with a vampire; the vampires usually could care less until they have the pack nipping at their heels. Real "Children of the Moon" also exist, but they are little more than a throwaway mention in the last chapters of Breaking Dawn, to differentiate the Quileutes from the vampires' ancient enemy.
True Blood makes werewolves relatives of "shifters", along with were-panthers, were-tigers etc all under the general heading of "two-natured" beings. Being a "were-something" is mostly genetic, and the books and HBO series apparently disagree on whether it's possible to become one (or something like it) by being bitten; the book says it's possible, but one bite won't do it, while the HBO series had it fail to work in the same situation. Being a shifter is purely genetic; you can't become one by being bitten, and apparently it is a dominant trait (the two children of Maudette Pickens with her non-shifter husband, including Sam Merlotte, are both shifters). There's a low-lying antagonism between vampires and all two-natured, but they're not sworn enemies.
Vampire Diaries apparently hasn't gone too deep into werewolves YET (other than that they exist and vampires fear them because they're actually a match for them, kind of like in Twilight), and I don't follow the show, so I can't speak too much for it.
All of this more recent fiction about vampires and werewolves is mostly along the lines of "wouldn't it be cool if... ", and "yes, but you have to deal with... ". That's ALL pretty recent; as recently as the early 1900s, even the rumor that someone was either of these things was cause for a lynch mob. It wasn't until later, with the rise of mass media and commercialization, that we come to the state of affairs we're at now.
