I have to say, I'm not sure if I really like any of the characters. Fyodor's behavior is bad and so is his lifestyle. Dmitry seems to be following in his father's footsteps, because of his "unruly" behavior and greediness. Alyosha is too "good." I feel like we haven't gotten to know Ivan as well as we did the rest of the characters. All I know about Ivan so far is that he is proud, educated and somewhat withdrawn.
I'd have to say my favorite character-- as many other people have already said-- is Alyosha. He does not judge nor condemn people as the others in the book, and he is willing to give up everything in order to follow something he believes in (becoming a Monk to follow God). Aloysha seems to be the only good member of the entire Karamazov family.
For obvious reasons, my least favorite character would have to be Fyodor. His constant drinking, wild ..uh.. "parties", and his bragging make me dislike him. He ignored his three sons and both of his wives ended up dead, probably as a result of the way he treated them. The only thing I like about Fyodor is that he seems to realize his behavior is wrong, and during his conversation with Aloysha, I felt bad for him. He is "wicked and sentimental."