Make a list of all the characters in your icons. (Although you may have more than one icon of a single character, they only go on the list once.) Alphabetize it. Take the first two people on the list; that's your first pairing. Second two people; second pairing, etc. Treat us to some commentary once you're done.
Azula and Detective Carlton Lassiter - That wouldn't happen until after Azula hit legal age. He seems to like crazy women, and Azula likes anyone she can manipulate.
Cheshire and Deadpool - I would ship it. They would be a dangerous, awesome pair of THE homicidal, violent couple.
Domino and June - They'd be good friends, good partners. June would likely think that Domino is crazy and find it hilarious that Dom is afraid of chickens.
Ozai and Patrick Jane - oh bloody crap no. No for so many reasons.
Piandao and Sokka - as canonly portrayed student and master
Toph and her awesome - 'Nuff said on that.