I have a really hard time ranking them because the ones that get on my nerves the most still have redeeming qualities and my favorites still have annoying foibles that make me want to smack them. I think that's a testament to the quality of their writing. That said, I'll try to rate them even though I haven't actually finished the game yet.
Dorian - I like him a lot and he has probably the least irksome flaws to me. He can be disrespectful and somewhat insulting to people, but it seems that he usually gets that way when the other party starts it rather than defaulting to being a jerk.
Blackwall - His archetype is pretty simple, but I really like it. I think his desire to redeem himself in his own eyes is very admirable, and I like that he can be so committed to that goal and still be ready to joke around with people and enjoy himself. Plus, he's a hottie. I do dislike the broad brush he paints all nobles with, especially since he doesn't seem to mind praising the Inquisitor despite his or her potential noble heritage.
Cassandra - I'm glad they made a religious type that is practical and not shackled by dogma. She's got faith and conviction, but she also shows moments of spiritual vulnerability. She's in favor of the Chantry because of the good that's at its heart rather than because of some blind faith. I like her character far more than I thought I would.
Varric - I like the growth that his character has gotten. For the most part he's easy going and accepting of other characters, he's still funny, but his regret over the events of DA2 make it seem like he's there for a better reason that "because fans liked him". He can occasionally be mean spirited though, but then he has been through a lot.
Vivienne - I don't see eye to eye with her on very many issues and I think that she goes out of her way to antagonize certain people, but she has decent support for several of her arguments, even if she's a bit too quick to assume that her own experiences are standard for every mage. Its really neat to see a character who's not only poised and powerful on the field of battle, but also among nobles.
Iron Bull - I haven't used him as much as I would like to have, but he's interesting. I like that he's neither blatantly pro-Qun or anti-Qun and instead sees benefits to both ways of life. He's a big brute with hidden depths, and that's neat to see. He's the first qunari that I've actually liked.
Cole - Again, I haven't used him very much. I like how devoted he is to helping people and I think his way of viewing the world and people in it are very interesting. I can't wait to use him more.
Solas - Solas is very smart and provides a very unique view of the world, but he can be snooty and dismissive of other people or groups when they don't have the benefit of his experience or knowledge. That said, I like him and I'm pleased that he's usually at least civil with everyone else, even when they're trying to antagonize him.
Sera - She's entertaining and wild. She's also rude, small minded, and stubborn. She refuses to see the merits of any mindset that's even slightly different from her own and that is one of my absolute greatest pet peeves. She irritates me in every one of our conversations, but even she has redeeming qualities.
I like all of the companions though. They're well written and there are at least a couple of things I like about each character.