Edit: Also, on an unrelated note, anyone want to talk about their favourite characters? It's something I've never (or rarely) see in here, so I'd love to see who you're excited to see every week, who you're rooting for, etc.
It's a rather difficult choice since I think most of the characters are rather interesting in some manner (I have an interest in pretty much everybody except Bran and Jon). Most of the time, this is very situational; it depends on the plotline that character is partaking in but if I had to choose I would probably go with Stannis and Melissandre. Stannis' extremely pedantic outlook and his stern determination make him an extremely compelling character to me, particularly when combined with his slight corruption at the hands of Melissandre. The power dynamic between the two is fascinating particularly with Melissandre so masterfully manipulating him into complete submission (the last episode has made this even more compelling to me with Melissandre's "and none have seen the blade" as now there is a threat present that I hadn't considered before) while simultaneously manipulating the magic into a narrative of her own creation ("You shouldn't have this power"; paraphrasing). They compliment each other very well and both actors are extremely competant at delivering the material presented to them. It also helps that they're the most prominent magic users in the show and that "The Lord of Light" plotline is my favourite plotline in the show. Regardless of the season, all characters bend the knee to Stannis for me; it's the one location that I consistently want to see more of. I would gladly watch an entire episode of Dragonstone.
After that I'm not particularly inclined towards any characters, it really does depend on the situation that they're in. Aria is another character that I have generally enjoyed watching over the three seasons but I feel the main positive to her plotline is that she regularly meets with interesting characters (Silvio, Jaqaen, Hot Pie, the brotherhood). I haven't found her material this season very compelling for her as a character but it has remained interesting due to the brotherhood (and introducing those characters is, I'm quite sure, what her primary purpose this season has been). Sansa is a character that I hadn't particularly cared for in the first season but the actor has been consistently delivering every single scene for the last two seasons and, as a result, I've been growing interestingly interested in the character. Her material this season continues to be intriguing (honestly, it's reached the stage where absolutely everything that can go horribly tragic for her, does go horribly tragic which I guess is amusing in a rather dark way) and the actor's competence is really shining. Whereas in the first season I didn't really care for her I now look forward to every scene she's featured in. I'm sure there will be a slight respite for her now that the maneouvering is over (surely...) but as of now I find her enjoyable. The Hound seems interesting but we've seen him so little that it's very hard to make any sort of judgement and the same holds true for Jaqean and the brotherhood. The Tyrells are incredible enjoyable to watch as they masterfully manipulate those around them and Olenna and Margaery are my favourite additions this season (I know Margaery was also in the previous season but not as a regular). Tywin continues to remain intriguing and his presence is felt in every scene. Jaime and Brienne interact marvellously together. Jaime's recent characterisation, by altering our perception of him using previously known information, has been done in a logical, natural manner and gives a very large insight into his outlook (although I'm expecting him to revert immediately back once he returns to King's Landing as Tywin continues to domineer the family). I enjoy Tyrion but at the moment I don't particularly care for seeing more of his scenes; I just feel there's more interesting plotlines elsewhere.
Until Carstark was executed for murdering the Lannister children I'd found Robb rather bland but by following through on the execution he's managed to slightly regain my attention. He's in a much more interesting situation and I'm eager to see with how he deals with it. For the first time I wouldn't mind if he actually wins the war. I had become interested in Theon last season and I like the internal conflict he has/had regarding his desire to be a Greyjoy and a Stark but this season? Incredibly dull. I dread further torture seasons, not because of the gruesome material but because his scenes are moving at a glacial pace which itself wouldn't be problem if the material was compelling but it's just incredibly tedius. I'm sure there'll be some form of payoff (there better be), and as a result I understand why it must be done, but that doesn't make this less dull in the present. Varys and Littlefinger remain enjoyable and I think they work well in the sidelines. Littlefinger's monologue this season remains a highlight for me. In some ways, I don't want to see much more of them. In the spotlight I don't know if they'd be as enjoyable as they are in the background and I think this suits their characters (both being incredibly powerful, both playing the game so well that they don't draw attention to themselves). They have both been developed very well. Danaerys is... inconsistent. She was one of my favourite characters in the first season and then the second season it just felt like a complete drag and now the quality of her scenes makes me apprehensive yet hopeful although I do enjoy Jorah.
My favourite characters (well, those I want to view more of) seem to be those with some form: of stern determination, an ability to manipulate others, a connection to The Lord of Light plotline, and a connection to the politics in King's Landing (my second favourite plotlines are those that revolve around this; the Sansa situation has been my favourite character plotline thus far this season). My least favourite characters are those with some relation to the North, the Starks (Aria a large exception and Robb a very slight exception) or the Wall; I just don't have much of an interest in the characters in that area even though I can see the appeal (the strongest characters in that area I feel are Osha and Hodor), they just aren't for me.
This was probably more thorough than you wanted. It's a testament to the show and the calibur of the actors that almost every character holds my interest in some manner. Don't mistake not currently being interested in seeing more scenes for a lack of interest in the character at large though, I certainly don't expect such a vast array of characters to be constantly engaged in compelling material.