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.
Angel/Christine (Phantom of the Opera) - She likes men with multiple faces.
Ethan/Faith - Dark and dangerous, I could see that (especially thanks to wickedfox)
Fred/Giles - I could really see them getting together. Drat, now I'm curious and am tempted to seek out fic with this pairing to read. It must exist. Giles has been paired with everyone.
Guildenstern/Illyria - Perhaps the strangest pairing this meme makes
Jareth (Labyrinth)/Jarod (Pretender) - No comment.
Jen (Dark Crystal)/Lily (Legend) - Both fantasy characters, even if one is a Gelfling
Lindsey/Lorne - Ewwwww
Miss Parker (Pretender)/Oz - Another strange one
Phantom/Player (Rosencrantz & Guildenstern are Dead) - Well, they both like the theatre.
Rosencrantz/Spike - Believe it or not, I could see that.
Tara/Veronica Franco (Dangerous Beauty) - They'd be beautiful together.
Willow/Xander - Just because I don't read or write it, doesn't mean I can't see it.
I've got more icons than this, but I didn't want to get into to much beastiality/otherworldly (dragon, unicorn, fairy) pairings.