District One Career and eventual victorObsidian who, despite his initial displays of coolness, can be downright awkward, especially when it comes to his Love Interest—Vale. See also: his rehearsal of how he would propose an alliance with Vale, as well as plenty of the not exactly cool things he says once he and Vale actually do team up.
Caramel of Assumptions becomes this trope whenever an attractive girl talks to him directly, constantly stuttering and flubbing his lines. Ironically, his main love interest grows fond of him since he doesn't act differently around her, though he does regress back into this after a few teases from her.
Luna: This is great! We cannot wait! Astronomical Observations! Telescope Calibration! And Trivia Pursuit! This should be a detonation! Is that the right wording? This should be a detonation? Celestia: ’This should be a blast’ is more commonly used.
Triptych Continuum has Twilight Sparkle, whose immediate reaction to seeing Rarity's eyes have changed colour is to start working out a comprehensive test for any changes in perception Rarity might have.
In Carrot Top's brief appearance, she mentions she once got so bored during Cider Season, which she usually spends on her own due to not being obsessive over apple cider, she started making dioramas out of carrots.
Cadence borrows a page from Twilight Sparkle's book at one point when Celestia agrees to officiate her wedding, and she starts hopping in a circle.
Princess Twilight Sparkle is very enthusiastic about learning and typically cheerful, but she's pretty socially awkward and stammers when an event doesn't go as planned (like dropping her papers and forgetting to use her magic to pick them up due to embarrassment).
Flash Sentry is typically well-composed, but when he's around his crush and protectee Twilight his grip on his emotions is loosened. When he unexpectedly bumps into Twilight in a hallway, he stumbles through his apology, bowed to her twice more than he should have, and then ran away to avoid making a bigger fool of himself, which is just one of the earliest examples.
When we first meet Spark Wheel of Without A Hive, he's a sweet, awkward orphan colt who builds toy robots and flying machines out of junk at his orphanage. When we meet him again as an adult, he's been adopted by a wealthy family who sent him to a technical school, and now he's working on a real flying machine decades in advance of Equestrian technology. He's still sweet and awkward, though.
Wheatley in the Portal 2 fic Test Of Humanity after becoming a cyborg (GLaDOS implanted his "brain" into a human body For Science!). Tall, nerdy-looking, clumsy, noticeably chubby, yet friendly and well-meaning. Even Chell admits she finds his awkward nature to be endearing and it's part of the reason she falls in love with him.
In the semi-genderbent fanfic The Kirita Chronicles, Kirigaya Kazuta, a.k.a. Kirita, the genderbent version of Kirito, has problems speaking with males. She tends to be more hesitant and stutters more when talking to them in comparison to how confident and strong she is when she is fighting monsters.