In Alex and the Ironic Gentleman, the mild-mannered English teacher with pirate ancestors, Mr. Underwood, is passionate about fencing and proper grammar, and doesn't hesitate to befriend ten-and-a-half-year-old Alex after accidentally running into her with his bike.
Karl Sadeghi, from the EDA 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.
Captain Carrot, though he doesn't look "dorky" at all. His awkwardness is mostly in the form of misunderstanding figures of speech and being overly enthusiastic about things nobody else cares about.
Death. Yup, you read that right. He is fascinated by humans and tries to emulate their behaviour, but can never really grasp the reasoning behind it. He tries so hard though, even if he never quite succeeds. Death also adores cats and has adopted quite a few.
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◊ in the films doesn't hurt.
Neville. 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.
Ron Weasley. Red hair, awkwardly tall and oblivious to love. He fangirls over famous Quidditch players, and is Harry's loyal companion and sidekick.
Hungry as a Wolf, the sequel to the Weird Western novella Sheep's Clothing, reveals that Wolf Cowrie, the grizzled, stoic hunter of the strange un the American frontier, turns into a stuttering mess in the presence of Susannah Twohill.
Sarah Martin from Kinda Super Gay. She often babbles, especially when she's lying. A good example is when she tells Marquez that she's a time traveller who'd come from the future to save the child who would win the fight against robot overlords. Marquez isn't convinced.
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. His behavior towards other people (including his grandfather) kind of reduces his "adorkable" qualities.
Michael Vey has the eponymous hero especially in the first book, which his girlfriend Taylor finds especially attractive, though as the books go on he becomes more hardened and grows into his leadership role. However, there are still moments where he becomes a Badass Adorable.
Elend Venture of Mistborn is a shy, gentle, and naive scholar who spends parties and balls reading, deliberately wears rumpled, too-large clothing to rebel against his tyrannical father, and attempts to avoid eligible young women - until superpowered heroine Vin meets him as part of an undercover operation and discovers that Nerds Are Sexy.
Amelia "Mia" Thermopolis from The Princess Diaries. Especially in the film adaptation where she's even more awkward and clumsy and wears glasses before getting contact lenses.
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.)
Brambleclaw is an obvious example especially as an apprentice being a ridiculously Keet Naïve Newcomer who's very energetic and eager to go on The Great Journey. This carries on to his days as ThunderClan's leader when he seems very energetic even though he's one of the oldest cats in the Clan.
Bumblestripe and his father, Graystripe could count as well. Both being genuinely Nice Guys who are best friends (and in Bumblestripe's case dating) the protagonists of their specific series. Both enjoy food and are a bit goofy and clumsy.
Self-confessed coward and Bookworm Sam is 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 Star Wars: 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 is awkward in personal relationships, self-depreciating 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-22, whose curious, giggle-prone and careless nature makes even the snarky, apathetic 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.
Doctor Watson in Sherlock Holmes has a few moments: for example, in A Study in Scarlet, when he is hurt when Holmes bashes C. Auguste Dupin, a fictional character he admires, and in The Sign of the Four, when he is smitten with Mary Morstan and so nervous that he can barely get his words out straight, and winds up telling her a story about how a shotgun stuck its head into his tent one night, and he shot a double-barreled tiger cub at it.
The Rainbow Magic series has Rachel's dad, who's endearing in his attempts to be cool and likes flowers, animals, and other cute things. He's clumsy, too.
Beatrice Löwenström in Överenskommelser has a nerdy side, but she's a Bad Ass Bookworm.
Ossian Bergman in De skandalösa is a nerdy scholar, who has a Sensitive Guy and Manly Man dynamic with the more roguish male protagonist Gabriel.
Dork Diaries has this as a central theme, as half of the cast are adorkable to some degree.
The heroine is praised for being "dorky, funny, and friendly".
Charlie Duskin from Chasing Charlie Duskin is one of the female cases. She's a huge music nerd, but so shy that she can't work up the nerve to make friends and only really comes alive when playing her guitar.
Kacey Caddell over in Serial 11 of Spectral Shadows is extremely shy, usually to the point of being unable to actually converse with those she doesn't know. She also spends loads of time on the computer (at one point feeling the effects of eye strain) doing things like playing Another Life, writing fanfics (of a sort), and researching information about lucidly dreaming and being in control of dreams.
Natalie Dashkov from Vampire Academy is a cute, dorky girl. Nice, plain, uninterested in social politics, with a somewhat endearing tendency to ramble on at length. Taken Up to Eleven in the movie due to her portrayal by Sarah Hyland.
Robin of The Girl from the Miracles District is incredibly trusting, bizzarely innocentnote He's a professional killer, and gets all flabbergasted when in company of scantily-clad women, blushing and losing his train of thoughts.