I'm a little out of my element with pairs (and even more so with ice dance), so I don't have too many favorites as far as the pairs are concerned and so like with the ladies, I am only going to hone in on one favorite, which has to be Xue Shen and Hongbo Zhao.
I think it is extremely impressive that they made the difficult transformation from being a pair that just had the big tricks to a pair that really captured the audience's hearts with their artistry. One performance of theirs that I particularly love is their freeskate at Worlds in 2004 - it is simply magical.
Also, as amazing as Shen and Zhao became as skaters, another reason that they're my favorite pair is their personal story *. The sacrifices they and their families made for them to get where they are now make their success all the more satisfying to see , and their love story is as close to a fairytale as true life can get. Their victory in Vancouver is definitely one of my favorite moments (if not THE favorite moment) of all the Olympic Games I have watched.
* There's no way that I can accurately summarize it here, as I haven't read the backstory in it's entirety for a good while, but the book The Second Mark features the detailed backstories of Shen and Zhao, as well Berezhnaya and Sikharulidze and Salé and Pelletier. I highly recommend reading if you have even a minor interest in any of those pairs or the 2002 Olympic scandal.