Aragorn vs Jaime Lannister: Jaime would win, dishonourably. We never learn what kind of swordsman Aragorn is, but even if they're equal Aragorn is too noble to be able to win over someone as tricky as Jaime.

Smaug vs Balerion: Smaug. Balerion is just an animal if he doesn't have a rider. Smaug is intelligent.

Saruman vs Melisanre: Saruman. No contest.

Wargs vs direwolves: I'm gonna say direwolves because I like them better. They're probably pretty even though. Unless the smart ones from The Hobbit are the ones we're talking about.

Ice vs Glamdring: Glamdring is magical right?

Frodo vs Tyrion: Tyrion would make Frodo his squire and Frodo would be happy about it.

Nazgûl vs White Walkers (Others!!): No idea what the Others can do yet. Except that there's lots of them. One Nazgûl vs one Other would probably go to the Nazgûl though. They fly.

Cave troll vs Mag the Mighty: Mag is smarter than your average cave troll.

Gimli vs The Mountain: Gimli is smarter, but the Mountain has killed smarter people before. Sorry, I'm betting on Clegane.

Ned Stark vs Boromir: This one is hard. Two good men ruined by their flaws, but in opposite directions. In a swordfight I'd say Boromir simply because he's younger and probably has more fighting experience. Besides, Ned is more a commander than a soldier.

Edit: Yup, he said pretty much what I though. :)