Off-hand, I would say that Frodo and Sam are the bravest.
They're two little Hobbits who've basically had no experience in the world outside of the Shire, and who volunteer to travel to the most dangerous place in all of Middle-earth in an attempt (not a certainty) to destroy The One Ring.
As for Frodo wanting to take the ring, I don't think it makes him any less brave than Sam. Hell, the same thing no doubt would have happened to Sam if Sam had been carrying the Ring for as long as Frodo. In fact if anything, Frodo might actually be said to be the braver one, because he was carrying the burden of the ring on top of everything else.
I don't think it's fair or accurate to say that Sam is better just because he wasn't corrupted by the ring (which, by the way, he was, if you read the book. Not severely corrupted, but tempted, and he hadn't even been carrying it for half as long as Frodo had.)
And sure Sam fought Shelob and carried Frodo up the mountain yada yada. But doing one specific thing doesn't mean that you're braver than another person just because they didn't do the same thing. Frodo fought off Shelob as well as he could (in the book and movie) but just because he didn't beat her doesn't mean he's less brave. Remember that bravery and courage means doing things you're afraid to do and acting in spite of that fear.
And was Frodo a coward for not physically being able to climb up Mt. Doom by himself? Hell no; he was burdened practically to death by the ring, by his travels, by being tormented by Orcs (which, may I remind you, Sam wasn't), so it's small wonder that, God forbid, he needed a little help climbing the mountain.
Far be it for me to assume what other people would think, but I'm fairly positive that even Sam himself would not see Frodo as less brave than himself (and yeah I know they were friends and Sam is a modest guy anyway, but still.)
So here you have two peaceful, maybe somewhat-naive Hobbits who, as a people, do not have the strongest, stoutest, or tallest physical stature - which is only one point against them as far as their task is concerned. Nevermind the bravery they had to muster, especially as it was only the two of them. They didn't have the comfort or guidance of Gandalf or Aragorn or any of the others.
So yes, I think Frodo and Sam were certainly the two bravest characters in the book/movie.