I've just been giving it some thought and I have pretty much decided which characters I like and which ones I don't.
My favourite character is Violet, The Dowager Countess. Maggie Smith's portrayal of her is superb and she truly has the best lines. Second favourite would be Lady Mary. I like that she is honest and fiesty and not afraid to speak her mind or tell the truth, regardless of how painful something might be. Next would be a tie between Mrs. Patmore and Lord Grantham as I think they are both excellent people.
Another character I loved to hate was Vera Bates. Maria Doyle Kennedy played her so well that I actually ended up liking her more than Bates.
Speaking of Bates, he is my least favourite character. 'Noble' people annoy me and I don't really think his storyline here in Season 3 has so far added anything important to the plot. That may change as the episodes progress but I just don't like Bates and would have been quite happy for him to hang - guilty or not.
Close behind Bates as my least favourite is Countess Cora. Her character is so bland and annoying. The only time I found her interesting was when she was dying of the Spanish Influenza. This may be partly due to the fact that I don't consider Elizabeth McGovern a particularly talented actress, and I never have, but I think it's more connected to my dislike of Cora's character.
I haven't got a definite third place for a character I dislike, but it would possibly be a toss up between Daisy and Thomas because they both annoy me for different reasons, still, that's how it's supposed to be - having some characters to dislike in any film or any television show is very important, it makes it interesting!