Whereas I can't imagine ever liking Linkin Park or any of their nu-metal cohorts in the near future, occasionaly I find myself suddenly liking music I couldn't stand before. Previously it was dance music when I was a metalhead, which I again don't really like.
My immediate candidate, however, is Aimee Mann. I remember hearing about her about 10 years ago in some PC magazine where they were giving out links to websites when the web was still new and exciting and not dominated by Google and spammers, and one such link was to her page (or fan page probably as bands didn't tend to have official ones then). I never bothered to find out who she was until a couple of years ago. And not being one to waste money on something I probably wouldn't like, it wasn't until when BitTorrent popped along that I decided to sample her wares. So I er, acquired an album, listened to it and wasn't greatly impressed. A couple of alright songs were on it, but nothing special. But gradually I found myself listening a bit more, until I procured one of her early albums. This I immediately took a dislike to for about a year. Yet once again, bit by bit it found itself on my playlist, mostly for background music. And now a year on, songs I gave 1/5 on Itunes, I suddenly really like. In fact I enjoy listening those 2 albums quite a bit. Remarkable how music can gradually ebb away at your resistance until you find yourself liking it. I know some albums are growers instead of instant hits, but a year? Crivvens!
Hot Fuss by The Killers. I liked Somebody Told Me, but hated everything else they'd released. Then for some reason I thought most of Hot Fuss was great, and found myself pre-ordering their new album as soon as it appeared on Amazon.
I quite often dislike something then find it a year later and love it. "Head Trip in Every Key," the Superdrag album took me about two years to get into. I bought it at the same time as the more instant "In the Valley of Dying Stars," but now Head Trip is one of my favourite albums ever and In The Valley isn't as much.
And irrelevant to the point of your post, but I t'ink Aimee Mann is quite good too.
Of course, people's opinions back then could have changed again. For example I hated Pickled Onion Monster munch crisps back then, but now I like them. No, actually, I still can't stand them. Bloody awful. Worse than Space Raiders.