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How about the Dresden Files series? I suppose you could think of them as fantasy if you want to, but they're set in modern day Chicago (and other places), starring a wizard/detective.
Midnight's Children might be right up your alley, it's kind of an Indian Forrest Gump with some superpowers in there for good measure. Er, emphasis on the "kind of," it's really good at any rate.
I hate to be that guy, but even though you said you don't like Sci-Fi, you should check out Ender's Game. It isn't really hardcore sci-fi but the many of the main characters are a certain type of down-to-earth super hero.
If you're generally okay with fantasy, I highly recommend Name of the Wind. The protaganist has those qualities.
I hate fantasy and The Name of the Wind is one of my favorite books, so +1 on that.
Here are some non sci-fi/fantasy recommendations, although in some cases it's not quite "supernatural" as much as it is "preternatural" or something similar, or the character just views themselves that way, or something like that, because frankly real life doesn't have a lot of people who are actually supernatural so most examples of those kind of people are in fantasy/sci fi (all of your examples are either fantasy/sci fi or people with mental illnesses): Invisible Man (by Ralph Ellison, not the sci-fi novel by Wells) Thus Spoke Zarathustra Pattern Recognition Motherless Brooklyn Catch-22, kind of. Crofton's Fire a little.
Flowers for Algernon might fit the bill - it's about a mentally disabled man who volunteers for an experimental operation to increase his intelligence.
Then there is terrible, heart-breaking sadness.
Also, if you like comedy (and if you can actually find a copy), The Bandy Papers are delightful. The series starts with Three Cheers for Me, and the protagonist, Bartholomew Bandy, is a young Canadian who joins up to fight in WWI. Bandy has all the makings of an excellent soldier: he's dedicated, highly skilled, extremely obedient, and supernaturally lucky. He also, unfortunately, has the unique ability to irritate the hell out of any senior officer in his immediate area, so he basically blunders from one forced suicide mission to the next, infuriating those in charge with his ability to survive.
They're detective stories set in a sort of steampunk world with things like elves and the like, but it doesn't get too far into fantasy. Kind of a Neil Gaiman sort of thing.
There's a whole internet of Mary Sue fanfiction out there for you to explore! *grin* Just kidding. It seems that the common thread that you enjoy in movies is the hero myth. It might be a good idea to read "The Hero with a Thousand Face" by Joseph Campbell. It's a non-fiction work that details the "monomyth" of the hero's journey, and the similarities between various cultural hero myths. It's very well-written (probably one of the more accessible versions of his works) and may give you some introspection as to why you find the hero myth so appealing.
I'm afraid that anything involving supernatural powers is at least partly fantasy. A lot of science fiction tends to be fantastic as well, since accepting the literary devices of science fiction requires the same suspension of disbelief for the "magic"/technology.
Dresden Files by Jim Butcher seems like it'd be a pretty good fit. The protagonist is a Wizard in modern Chicago and struggles with both the mundane and the more mystical, and how the two interact. I'd probably label him as a super hero all things considered.
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I hate fantasy and The Name of the Wind is one of my favorite books, so +1 on that.
Here are some non sci-fi/fantasy recommendations, although in some cases it's not quite "supernatural" as much as it is "preternatural" or something similar, or the character just views themselves that way, or something like that, because frankly real life doesn't have a lot of people who are actually supernatural so most examples of those kind of people are in fantasy/sci fi (all of your examples are either fantasy/sci fi or people with mental illnesses):
Invisible Man (by Ralph Ellison, not the sci-fi novel by Wells)
Thus Spoke Zarathustra
Pattern Recognition
Motherless Brooklyn
Catch-22, kind of.
Crofton's Fire a little.
Also, if you like comedy (and if you can actually find a copy), The Bandy Papers are delightful. The series starts with Three Cheers for Me, and the protagonist, Bartholomew Bandy, is a young Canadian who joins up to fight in WWI. Bandy has all the makings of an excellent soldier: he's dedicated, highly skilled, extremely obedient, and supernaturally lucky. He also, unfortunately, has the unique ability to irritate the hell out of any senior officer in his immediate area, so he basically blunders from one forced suicide mission to the next, infuriating those in charge with his ability to survive.
Also, at one point he loses a fight to a bathtub.
They're detective stories set in a sort of steampunk world with things like elves and the like, but it doesn't get too far into fantasy. Kind of a Neil Gaiman sort of thing.
At the very least, its fairly unique.
I'm afraid that anything involving supernatural powers is at least partly fantasy. A lot of science fiction tends to be fantastic as well, since accepting the literary devices of science fiction requires the same suspension of disbelief for the "magic"/technology.
Control Switch On (Ira Teller) needn't be purchased. It's readily available to download in pdf form.
Boom
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http://www.amazon.com/Choke-Chuck-Palahniuk/dp/0385720920
Not exactly what you are looking for, but it seems related somehow.
but they're listening to every word I say