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.
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 is Harry's loyal companion and sidekick.
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.
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.)
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 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 Minds 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.
Beatrice Löwenström in Överenskommelser has a nerdy side and is attractive. She's a Bad Ass Bookworm too.
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.