Let me start off by saying that this is not an exhaustive list. I read every day — to some extent anyway — and therefore my choice of who makes the best hero is likely going to change over time.
Hero – a man of distinguished courage and ability, admired for his brave deeds and noble qualities. (Author’s addition — someone with the oomph to carry a story for 300 pages or more.)
Coming in first place is James Alexander Malcolm Mackenzie Fraser (AKA Jamie) from the Outlander series by Diana Gabaldon. Taking away the swoon factor of a giant red-headed, sword-and-musket-wielding Highlander, Jamie has this vulnerable quality that just makes me want to give him a big hug. He’s got bravado and gumption, and I’m pretty sure he’s just as bad at strategy as I am because he sort of just does things. (Like march into an angry mob and try to save an accused witch from being killed.)
Second place goes to Kelsier from Brandon Sanderson’s Mistorborn – The Final Empire. No, I didn’t pick Vin or Elund (the two you might expect me to pick from that book) because they irritated me at some point or another. Vin because she got a little whiny about where she came from and Elund because … yeah … he didn’t get all that much page-time in the book. But Kelsier … Kelsier was my favorite. And my coworkers can attest to the fact that I fairly squealed and spun in my chair a few times during the battle moments there at the end. (I don’t want to spoil it, but I’m a girl and even I was impressed with the magic fight.)
The number 3 position goes to Nathaniel Bonner from Sara Donati’s Into the Wild. Sweet, holy bananas! What I wouldn’t give for that man to comment about my boots. There’s nothing particularly extraordinary about Nathaniel, he can’t use magic and he doesn’t use a sword, but he is super smart and I’m pretty sure he makes up for the no-sword thing with the tomahawk.
Coming in at the fourth position is William Harindale. I know, I know, he’s 17 or so, but the boy has “hero” written all over him. He stars in Cassandra Clare’s Infernal Devices series and he’s the first character to make me cry in a long time. (No, I’m not going to tell you which part made me weepy. )
I had a hard time coming up with a fifth hero. I almost bent the rules and dove into film and TV heroes, which would have given me people like James T. Kirk and Han Solo to pick from, but I’ve decided that film heroes deserve their own segment. Heck, Star Trek deserves its own segment of Captains to fight between. So! I chose for the final hero … Harry Potter.
Yes, yes, good old Harry Potter. But there’s a reason why everyone loved him enough to stick with him for 7 books. Young, fresh, tragic, lost, and pit up against insurmountable odds … Yeah. Harry counts as one of my top 5.
That’s it! That’s my top 5. Who are yours?
AJMaguire 
Always fun to discuss heroes. In reverse order:
5. Sir Gareth Beaumains – the good one of the Orkney brothers from La Morte D’Arthur.
4. Carrot Ironfoundersson – From Terry Pratchett’s Discworld books. Absolutely hilarious, and such a nice guy.
3. Neville Longbottom – from the Harry Potter books. He’s not the chosen one, he’s not really one of Harry’s close circle, but he still stands up against the bad guys.
2. Eddard Stark – From George R.R. Martin’s Game of Thrones. A classic tragic hero. He tries to do the right thing, but playing fair doesn’t lend itself to winning.
1. Atticus Finch – From Harper Lee’s To Kill a Mockingbird (I know not SF or Fantasy). To my mind he is one of the great heroes. He has no special powers, and he takes on a challenge he can’t hope to win, and for which he stands against popular opinion. But he does it because it is the right thing to do.
I loved Neville, too! And I totally agree on Atticus Finch. He really was spectacular, even without magic, swords, or tomahawks.