Audrey, Wait! has James, who has an endearing work ethic that results in him being socially clumsy around Audrey. Also Audrey herself, who is unafraid to dance and sing (poorly) in public to songs she likes (and she likes a lot of music).
Also, Karl Sadeghi, from The Year Of Intelligent Tigers: he's shy, bespectacled, has a stutter, and is basically the biggest music geek ever. And considering how touchy-feely he and the Doctor get with each other, it seems that the Doctor sees the appeal.
The vampire Kostya in Night Watch is a pretty sensitive, nice guy, and there's a scene in Twilight Watch where Anton at first thinks he did a Charm Person on a woman to make her very helpful, but then realizes it was his natural dorky charm.
Harry Potter. He's a scrawny boy with perpetually messy hair and glasses who, for most of the series, can't talk to girls romantically without making an idiot of himself.
Bushy-haired Bookworm Hermione, who stutters approximately a third of everything she says.
Luna Lovegood. Her Cloudcuckoolander nature is a big part of it, but it was cemented by her all too brief time as a Quidditch announcer. Being played by Evanna Lynch◊ doesn't hurt.
Neville does qualify. In the beginning books, He's awkward, clumsy, and can't do anything right. Then, in Harry Potter and the Order of the Phoenix, you find out Neville's parents were tortured into insanity by Bellatrix Lestrange and you can't help but love the guy. Finally, for the dorks in all of us, he loves plants.
Marius from Les Misérables. He's so completely shy that when he sees a pretty girl, he tries to go up and speak to her but runs out of nerve on the way.
Of course, his behavior towards other people (including his grandfather) kind of reduces his "adorkable" qualities.
Butters from The Dresden Files. "Polka will never die!" No, Butters. It won't.
Ivy; half eight-year-old, half ancient repository of all human knowledge.
Amelia "Mia" Thermopolis from The Princess Diaries. Especially in the film adaption where she's even more awkward and clumsy and wears glasses before getting contact lenses.
Evan Tolliver from The 39 Clues. It's been told that's his girlfriend's secret nickname for him.
Shannon Foraker from the Honor Harrington series is a socially-inept technonerd who early on has a hard time keeping track of politics that would have literally endangered her life if not for the captains who valued her wizardry with electronics. (And she still has a hard time keeping track of her wristcomm.)
Ed Hamner, Jr. from Stephen King's short story I Know What You Need is described to be this.
A Song of Ice and Fire: The squire Podrick Payne is a Crouching Moron, Hidden Badass who never fails to stumble over his own words. Self-confessed coward Sam is also quite sweet, and is about as close as you're going to get to a medieval nerd.
Richard Mayhew from Neverwhere has this going on, with his initial propensity to get pushed around, his collection of trolls (that got started by accident), and his tendency to look like he's only just woken up. The latter is Lampshaded as making him more attractive to the opposite sex than he'll ever understand or believe.
As a young man, Luke Skywalker is often endearingly new to the bigger galaxy, naive and completely unused to deception. It's pretty clear in Allegiance that he barely knows how to conceal something; in Choices Of One that he hates killing; in Rebel Force he's unpracticed and clumsy with sarcasm; and in Splinter of the Mind's Eye he's a pure foil to Leia's cynical outlook.
Tash Arranda in Galaxy of Fear is adorably thrilled to meet Luke, becoming unusually shy in his presence.
Trapped on Draconica: Kalak believe it or not is this; awkward in personal relationships, self-depricating and doesn't know how to talk to a girl.
Elder from Across the Universe. He's a sixteen-year-old guy who is trying to lead a ship full of people, has a tendency to fumble things up, and completely goes to pieces around Fiery Redhead Amy, bringing her flowers when she first wakes up and getting nervous when he has to hold her as they ride in an air tube.
Orr from Catch Twenty Two, whose curious, giggle-prone and careless nature makes even the snarky, apathic protagonist Yossarian want to hug him. It helps that his constant and comical habit of crashing his planes into the ocean wound up being all part of his plan to escape the military.
