As people have said, Darla/Angelus and Spike/Drusilla are the longest running couples for sheer time. Can't comment on DH or any of the comics, as I've not read them.
Zoe/Wash were probably Firefly's longest running couple, thought as a new relationship begins at the end of Serenity, it's impossible to say how long that would have lasted.
Xander/Anya was a couple for quite a while, and Willow/Tara. Buffy/Angel always seems to flare up again when they're around each other, but I don't know if we can count them as being in a relationship after Season 3, since they're apart from each other the majority of the time, and both have their share of other relationships, or potential ones. Kennedy/Willow, once again, could have gone on for a long time after the show's end (and indeed, it seems to have from what I've heard of the comics).