1. Conan the Cimmerian (Robert Howard's novels, Conan movies) versus Indiana Jones (Indiana Jones movies)
Indy wins this one. He's smarter, more resourceful (only just) and has infinitely more style.
2. Batman (Batman comics, Batman movies) versus Odysseus (mythology)
Batman. Solely through the technological edge.
3. Sherlock Holmes versus Gandalf the Grey
Argo summed this one up. They have tea, discuss the matter, and Gandalf decides to let the mortals handle the affairs for a bit longer. So he wins, while Holmes goes back to the mortal world straight away.
4. Captain James T. Kirk (Star Trek) versus The Hulk
HULK SMASH! HULK SMASH YOU ALL!
5. Robin Hood (mythology, movies) versus King Arthur (mythology, various novels)
Nyargh! Robin Hood snipes out King Arthur and goes on.
6. Luke Skywalker (Star Wars) versus Samwise Gamgee (Lord of the Rings)
Nyargh AGAIN! The coin has spoken, and Luke wins.
7. Buffy Summers (Buffy the Vampire Slayer) versus Han Solo (Star Wars)
Buffy wins this. More of a hero, bolder, and also gives this competition a much needed hottie factor.
8. Spider-Man (comics, movies, TV shows) versus James Bond (movies, Ian Fleming's stories)
Great power, great responsibility and all that jazz are no match for a PPK, killer looks and Q departments latest funky development. Bond wins.