The titular badger from The Urthblood Saga. This is one of Urthblood's main traits, and he almost never shows any strong emotions, or any emotions at all, throughout the saga.
Minato in Fairly English Story has brain damage from the car crash that left him orphaned. It results in his face being unable to react to his emotions and show them so he has to actively make the face that he is feeling. These also leads to the more emotion/pain he's in the more stoic he is.
Helyse Blake from the A Nightmare on Elm Street fanfic "Tainted Dreams" (at the beginning she was really unable to feel much emotions. Recently she is being able to feel more than in the earlier chapters, but she still doesn't show them too much. Maybe she has forgotten how to?).
The author has confirmed that there is a reason for her to be like this (not just because "it is cool") and that it will be told in future chapters.
Lieutenant Commander T'Var in The Wrong Reflection reacts with typical Vulcan stoicism to being involved in a battle where the fleet her ship was in suffered 92% casualties* counting ships that were damaged and repairable as well as those destroyed. She basically says they gave as good as they got and that she's satisfied with their performance.
She's far from rude and manages the occasional, but Caitlin strives to be this in Pokemon Black & White: Tale of a Legend. She must remind herself not to become overly excited, as she fears that getting too emotional will lead her to make rash decisions and jeopardize her team's safety.
In Nightblade, Nick, by virtue of being a sociopath. While he literally can't feel guilt or remorse for things he's done, up to and including murder, the rest of it is learned as a coping mechanism with abandonment.
Monsters In Paradise: Ellen Harrison, daughter of the Rustboro Public Library's librarian; she keeps her cool well enough that not even a rampaging bicycle in the library and a youkai crashing onto her desk back-first will dent her half-lidded stare. However, her stoicism is quickly shown to hide her frustration at both being unable to leave Rustboro, and her constant desire to learn being completely unnatural.
Domoverse: Isaac. Having grown up Amish, he learned that fighting back was evil and to trust in God. So after being kidnapped he quietly worked for the villain believing that it wouldn't be too bad, and once he was done he could go home. When he learned he wasn't going home and he was working for a mass murderer, he simply refused to work, prayed until he collapsed from exhaustion, didn't resist being beaten and only drank water. Even after Sadist got creative and forced Isaac to work, he kept his stoic resolve. He was eventually broken, but even then a glimmer of the stoicism remained as he planned the destruction of Sadist.
Code Geass Colorless Memories Rai the main character he tends to remain calm, act in a sedate manner and seems to be generally introverted Rai gives off more than a hint of this trope in general.
Though Rai has a few Not So Stoic moments sprinkled in the fic, most potently in Chapter 17 when he is finally reunited with E.E his contractor whom he smiled and rushed over to her which threw E.E off track for a second.
In Chrysalis Visits The Hague, the pathologist Edith is described like that by other characters, even getting nicknamed "Pokerface". Noticeably, this even becomes obvious in the parts told from her own perspective:
"It was obvious that [Princess Luna] had expected more of a visceral reaction out of the forensic.
'Ive seen worse.' [Edith] repeated, all while trying not to sound too heartless."