Ooooh nice idea of a thread! Where to start...
Well the main character that come to mind is Angel. At worse I disliked him on BtVS, at best he was just boring. Once I decided myself to watch his own series(took a while because of exactly what i'm talking about) it all changed though. He finally had more substance... showed a really different(and funny side)part of him which I LOVED. And it just got better over the seasons. So without a doubt, Angel is the most important character for me that went from almost hated to loved.
Outside of that... No characters had such a drastic change for me, but a few I didn't like got more interesting, so much as I like them now. Gunn for example, was pretty boring at start and I was wondering if I could ever feel anything for him. For me it started in 'That Old Gang of Mine' and from there he was pretty interesting. I particulary liked his storyline in the last season.
Aside of that for AtS, I could only mention Cordy... but I didn't hate or dislike her in BtVS. Just didn't have much interest in the character. But in Angel she's AWESOME, my fav character after Lorne. Kinda like Wes(but to a lesser extent) she progressed through the seasons(at least the first three for her), and she was the best friend Angel could ever have.
On BtVS, Anya, Spike and Andrew, I actually didn't like any of them much when they first appeared and did a few episodes, but as the time went, Anya grew on me, Spike became hilariously good(so much i'm ashamed to put his name on this list haha) and Andrew was funny and a good addition to the Scoobies in s7.
That's pretty much it.