Before I finish wading through ALL the replies, I had to choose Aragorn. Question was, who's the better fighter, and it's got to be Aragorn, hands down.
Legolas is the most awesome with a bow, no doubt, and those knives are very lethal, too, but Aragorn has successfully used a bow (remember Moria), any sword he lays hands on, daggars, fists, even his head (poor boy)... so
overall Aragorn is the better fighter.
All the others have their strengths, too, no doubt of that. So I can see why others might chose them in this poll, but the question was pretty specific, and I think that Aragorn is simply the only answer.
Edited to add: I had a bunch more to say after seeing your answers, but it got lost in my old computer. Just finished setting up my new one, so I think we should keep this discussion going... it's great!