A lot of people have pointed out Hawkeye as a mundane hero example. I just wanted to note that in dnd terms, Hawkeye would definately be magical.
He NEVER misses with his shots, no matter what he's facing. And the distance on his shots is unreal. Further, he can place explosives and other things on his arrows that in Dnd terms would be spell effects.
Now...you could flavor him as nonmagical. But in dnd terms you would stat him as a magical character....probably a ranger would get you closest.
Of course this brings up the semantic debate over what is magical? Is, say, 3e barbarian rage magical? Is the flight capabilities of various monsters magical? So on and so forth.
Heck, even in the HP debate, we see similar things. Do PC's get healthier or do they get better at dodging attacks? If they get better at dodging, why does it take longer to heal? Shouldn't healing rates either be a flat amount of time (say, X% of HP/day) or based on the type of wounds you take? Which in turn would make combat a LOT more complex. If HP are a measure of luck, though, then why is healing so wonky? Luck has a recharge rate?
If my fighter can wade through 20 normal humans, is he magical or not? Depending on edition, I could wade through 20 normal humans in about 18 seconds. Seems pretty magical to me. Certainly cinematic. So, is Whirlwind attack, or the 1e feature where fighters gain bonus attacks equal to their level against less than 1HD opponents, magic or not? It's certainly beyond human capabilities.
Yes, I realise that a master swordsman might take on 20 normal humans. Let's see him do it three times in a row. Because my 20th level fighter certainly can.
Here's 3 olympic fencing masters vs 50 opponents. They do down 48 of them, but, they still lose.
[video=youtube_share;PgKg0Hc7YIA]http://youtu.be/PgKg0Hc7YIA[/video]