Well I just watched the series from episode 1 to the end within a week, and of course I can't wait till the next season. Just like everyone else my top characters Tyrion. But Khaleesi is def my favorite character that grew the most. She went from being a shy and kind-hearted princess who knew nothing of men or war. To a strong, leader-type girl...with dragons! (And shes hot).
I couldn't stand however how Season 1 ended with Robb moving his army to King's Landing, And at the end of season 2 they have still yet to attack. Just seems like so much is happening but they are just sitting still for no aparent reason.
Arya is another character I can't wait to see where she ends up, her connection with Jaqen, who I can see playing a huge role soon in the series