When I was first introduced to the world of Harry Potter (watching the first three films in one day, which included going to see the third on its release at a local cinema), I was quite drawn to Harry/Hermione, if I'm honest. I guess just being a bit old-fashioned and thinking that it's right for the hero and heroine to pair off together. This despite soon learning that it was a doomed ship. I still clung to it...
These days, I'm more slash-oriented, and Sirius and Remus is my number one OTP ever in any fandom - I just think there's something wonderfully sweet about them together, and they're almost but not quite canonical, and I've got a little happy place where they survived the events of the books and they're living together in a cottage in Gloucestershire, where they're often visited by their adopted son Harry, on leave from teaching Defence Against the Dark Arts at Hogwarts. (I've got to write that one day.)
Also, Ianto Jones with...well, anyone other than Jack (who I'm convinced is going to break his heart), from any fandom I'm particularly fond of pairing him with George from Being Human and Sam from Supernatural, and one day I'm going to write my Big Slashy Epic Crossover which combines all three series and pairings into one...mess, probably.
And I really love Merlin/Arthur, but heck, that's canonical, so I don't have to want to see it. *g*