I don't know about the rest of the nerdfighers, but when I read a book, the big draw is the relationships between the characters in those books. So I figured I might start with the basics and go with the first relationship people seem to think of: romantic ones.
Personally, I'm a sucker for sweet but tragic romances, like Collins and Angel from Rent. My favorite at the moment is Hiroki Sugimura and Kayoko Kotohiki from Koushun Takami's Battle Royale. The extension in their relationship (and lives) that they get in the manga adaption absolutely broke my heart.
How about everybody else?
(Please note that I'm not talking about fanfiction-esque shipping, but canon romantic relationships from the source text, whether they were brief or happily-ever-after)
Oh God, I second Mulder and Scully ad infinitum. I still haven't recovered.
My favourite book couple of all time is Anne and Gilbert from L. M. Montgomery's ANNE OF GREEN GABLES series. I have many other favourite relationships in books, but as a couple I think Anne and Gilbert are tops.
Hunter and Morgan from the book series Sweep is probably my most favorite. Everything they have to go through and the strength and depth of their feelings, the length in which they would go to for each other is just fantastical and yet grounded in reality. one heavily involved in Wicca and Magic, but still.
Ron and Hermione- all I'm going to say is: TOOK YOU LONG ENOUGH! geeze....
(I'm a bit of a Hopeless Romantic if you couldn't tell...)
oh crap, see this is what you get for skimming the topic. ummm, okay, omit Bender&Claire, Quirrellmort, R&H AVPM version, Lloyd and Diane, Max and Logan, Max and Alec, and Buffy and Spike when reading...
I have to say Satou and Misaki from Welcome to the NHK, the novel at least. That's a doomed romance just waiting to happen - the romance is already there but you can't help but wonder just how screwed up it really is for them. They sign a contract with each other just so they won't kill themselves. Seriously, that's messed up.
Arthur and Gatty from the Arthur trilogy (The Seeing Stone, At The Crossing Places, King of the Middle March) by Kevin Crossley-Holland. Sure, they didn't actually hook up or get further than being close friends, but they really should have... Damned social classes!