Frodo ( and no, I am not a hobbit fancier by any means
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Because he is the one who gave up the most to complete his task, and if he hadn't, Middle Earth would have most definitely been lost forever.
All those other characters are very heroic, and they should all be very proud of their accomplishments... But as many have said they were in a way born and bred to be heros, to go into battle etc...
But Frodo had no idea when he was just a young little hobbit that he would get involved with something so much bigger than him. He never knew that he would travel to places that he never thought he would go to, and he never thought that he would basically give up his life to save Middle Earth and all the peoples of it.
For me being a hero is not just being extremely strong, or amazingly talented in the many tasks required in battle. It is how much you will give up, and how brave you will be to get a task done, or affect someones life (or a whole bunch of peoples lives).
Frodo is the hero who is the greatest of all the ages because he gave up the most that he could possibly give up (basically he gave up his future), and he did something that was totally unexpected of him and his kind