Everybody likes Tyrion, that's kind of a given. House Lannister is awesome man, I probably like them so much cause they remind me a bit of the Imperials. Tywin is a mastermind, Jaime has some of the best character development in the series, Cersei (hate that woman, but it's fun to see her get screwed, and Lena is gorgeous), and then there is Tyrion, but then agin, everybody likes him. There isn't much point in saying why because it's always the same reason
I really, really dislike Daenerys. I almost hate her. Which is a shame, since I like all the characters that are or were around her, with the exception of Mormont.
I also hated Jon Snow until ADWD, but... Well, you know.
And I hate Selyse Florent, hated Robb Stark, hate Hizdahr zo Loraq, hated Renly Baratheon.
"...he had EDDARD STARK beheaded..." I'm not so sure... Someone may have influenced him...
Pretty standard I guess. I like Jon, Arya, Tyrion, Jaime, Sam, Ser Barristan Selmy, and Davos. Don't like Cersei, Walder Frey, Lysa Tully, Viserys, Joffrey, Ramsay, Gregor Clegane, Melisandre, or Selyse Florent. Probably a fair few others I'm forgetting as well, but those are most of the big ones.
This is also based on likability of the people themselves. Some of the characters I dislike are actually some of the ones I think are most interesting or best written. I think Sansa is a fascinating character for instance, even though her chapters are often dull and her thought processes can be pretty annoying (especially in the first couple of books/seasons).
Also, I'm basing more off the books than the show, because there are some differences. (Daario Naharis, anyone?) Stannis is a lot more interesting -- and a fair bit more likable -- in the books as well.
On the other side, I like Stannis, Davos, Selmy, Littlefinger, Varys, Roose Bolton, Arya, Sansa, Melisandre, Victarion and Euron Greyjoy, Doran Martell, Cersei, Jaime, Areo Hotah, Brienne, Jon Connington, Wyman Manderly and Tyrion. (What can I do? So many great characters...)
And I liked Tywin, Catelyn, Rodrik Cassel, Ned, Oberyn, Maester Luwin and Aemon.
[EDIT] And how could I forget.. I also love Dolorous Edd...