Chris D'Amico/Red Mist could be a villainous example, given his love of comic books, his slight lisp and the fact that he and Dave have a silly bonding moment jamming in Chris's car while on the way to a crime scene. Unfortunately, his lovable dorkiness disappears pretty quickly afterwards.
Abe Sapien was always the smart one of the group in Hellboy, but it wasn't until the sequel he became full-on adorkable. It might have something to do with gaining his first love interest (any time he interacts with her is stuffed full of awkward), but even before that he can be seen geeking out over some rare Victorian goggles. Fangirls are split somewhat between this portrayal and the more traditionally Badass character in the comics.
Jane's usually a level-headed girl, but anytime Thor turns on the charm, she turns to a giggling school girl. Being played by Natalie Portman certainly didn't hurt.
Thor himself applies when he's on Earth. Despite being completely ignorant to how the mortal world works, he is a polite and chivalrous gentleman towards women, Jane in particular, even before his redemption. He even kisses Jane's hand and bows in farewell to Darcy and Erik for their help.
The Warriors Three and Sif demonstrated adorkability tapping on the glass window with huge grins when they found Thor.
Charles Xavier was a cute geek in his childhood, as demonstrated by the framed pictures of his favourite scientists next to his bed. As an adult, he uses his nerdy knowledge to woo girls at bars.
Hank McCoy. Soft spoken, stutters, asks Raven Darkholme out on the pretext of getting a blood sample and then apologizes for being forward.
Griff The Invisible is probably the shyest, meekest, sweetest wannabe-superhero you will ever meet, and fulfils this trope to the point that you almost need a teddy bear while watching so you'll have something to huggle when he's sad. Also his love interest/self-appointed sidekick Melody, a klutzy but very sincere girl with no comprehension of social norms and a lot of strange psuedo-scientific theories. Watching them dash around playing superhero is cute to a possibly lethal degree.
James Spader as Dr. Daniel Jackson in Stargate. He looks cute and vulnerable, and he's a geeky and quirky linguist, specializing in ancient languages. And he wears round glasses and looks like John Lennon.
Sir Galahad the Pure/Chaste. Zoot and other ladies from Castle Antrax find him irresistible. Unfortunately, they scare him off by being too advancing (they even ask him to spank them). When he seems like he might get into the mood, he's "saved" by one of his friends.
Sir Robin the Not-Quite-So-Brave-As-Sir-Lancelot. How else do you explain that his favourite minstrels and his group still followed him, even though when he ran away from the danger instead of fighting?
Elliot from Bedazzled (2000) is adorkaable, at least at first. Although it's rather negative in that he has no friends and his co-workers actively avoid him because of it, this movie needs a diabetes warning.
Mark Ruffalo as Dr. Bruce Banner. Quiet, nerdy, wears glasses, has rumpled hair, and a slightly nervous demeanor, as he's working for a company he doesn't exactly trust, with other super-powered people who won't get along, and he's trying his hardest to stay calm and not to let "The Big Guy" out. Also, he rides a tiny motorcycle at one point. And with the return of the previously mentioned Steve Rogers and Thor, the film is just FULL of adorkable-ness.
Iron Man: Tony Stark. While he's a snarker and showboater in public, his adorkableness is on full throttle when he's around the few close people he has, teasing them and giving them nicknames. (Like Rhodey.)
Ragetti also counts, particularly in the second and third movies. He's awkward, has strange moments of comedic intelligence, and has gained a rather large fan following. His adorkability is solidified in the third movie, when he hesitantly and sweetly speaks to Calypso "as to a lover".
Chekov, the ship's seventeen-year-old Russian whiz-kid who speaks with a funny accent, gets over-excited and runs in the most adorkable way possible. Taken Up to Eleven in the sequel, in which he gains super adorkable goggles.
"I ken do zat!"
Spock definitely has his moments, especially when he's around his girlfriend, Uhura. Helps that he doesn't seem to comprehend human sense of humour.
Uhura: Are you sure you don't want me to go instead?
Spock: That would be highly illogical as I am already outfitted-
Uhura Spock, I was kidding.
Spock: Uh... [looks adorkably confused as Uhura kisses his helmet]
Detective Alma Dray from Now You See Me when it comes to magic. She looks delighted after pulling off a card trick and claps enthusiastically during the Horsemen's show.
Elaine May's character in A New Leaf. Not only is she socially awkward, but she also forgets to take price tags off her clothes; spills multiple cups of tea in one sitting; has to be vacuumed after she eats; doesn't know how to put on a nightgown ("You've got your head in the arm hole") ... and she's a botanist.
Martin Freeman plays Bilbo Baggins as this in The Hobbit. He was also pretty adorkable in the original novel, what with his fondness for flowers, maps, and calligraphy and a Cowardly Lion personality that manages to combine bumbling with Guile Hero cleverness, but the films take it Up to Eleven. He faints at Bofur's description of death by dragonfire, mutters nervously to himself a lot, is very nervous about (and mildly allergic to) horses, and he's a Motor Mouth with a tendency to stutter and funny physical mannerisms.
The hero of Bringing Up Baby is a young, handsome, yet nerdy and somewhat ditzy scientists — an irresistible combination for the female lead.
In Teenage Mutant Ninja Turtles (2014), there are a few times when the turtles really do act like teenagers, treating their own exploits like kids would. A particularly funny moment has the group in an elevator right before the climax and they all start beatboxing and using their weapons as instruments in turn, including Raph and Leo. Another funny moment had Donatello wonder if his telescoping staff had the punch to flip a humvee, and as it does so in slow motion the camera lingers on his glee-filled face.
The Imitation Game: Some of Alan's scenes with Joan are geeky, slightly awkward and utterly endearing. For instance, they have lunch together outside in what appears to be a picnic date, but they are solving complex mathematical equations. Alan later steals encrypted messages from Bletchley Park, throws little rocks at Joan's window as if he were a would-be suitor, and then sneaks into her room past visiting hours to see if they can find a pattern that can help them break the Enigma code. When Clarke's parents pressure her to quit her job to get married, Turing proposes to Joan on the spot despite not being fully dressed (his shirt is untucked while his suspenders are loose) and there is still a little bit of shaving cream on his face; he then creates a makeshift engagement ring from a string that he finds in his pocket.