In the Dating SimAlways Remember Me, one of the love interests is a shy, but adorkable guy who is more comfortable texting than speaking with the protagonist in person. He also blushes quite a bit around her, and is the secret admirer sending her encouraging emails.
The remake of Final Fantasy III has Arc who is initially seen being bullied by children who appear to be younger than him and generally being being quiet and withdrawn. He grows more confident over the course of the journey.
The Manakete Myrrh in Fire Emblem: The Sacred Stones: she's been sheltered and revered as a living goddess in Caer Pelyn her whole life and leaving home brings her quite the misfortune until she's rescued by Ephraim. Also the Big Bad Lyon actually was this. It is heavily implied that he never have any friend because of his shy nature, that the Renais twins are his only friends. Uniquely, overlaps with Purple Is Powerful. He is THE strongest mage in Magvel universe, bar none, yet his personality is still insecure, timid and shy.
Path of Radiance brings us Astrid, a sheltered noblewoman who, though she wants to prove herself, fits this quite perfectly, she even looks like Hinata. Nephenee also fits this trope, which makes both characters Ensemble Dark Horses.
From Awakening there is Olivia, a rare case of a dancer with performance anxiety. She sports an almost perpetual Luminescent Blush because of her general shyness. It's lampshaded with her title in the "Where Are They Now?" Epilogue during the ending credits: Shrinking Violet. Inigo also has shades of this trope, though he normally covers it up well enough unless someone catches him dancing.
From Fates Princess Sakura of Hoshido stands out of being this trope because she can't even speak without stuttering. It is also implied it runs in the family. Her older sister Hinoka flat-out says she was like Sakura in her support with Sakura, and several of Sakura's older brother Takumi's other supports and other characters' dialogues imply he was this too. His current personality when the game takes place, however..
Arisu Kusunoki in Grimoire Private Magical School Academy is one of the more extreme example of the trope. One of the residents Token Mini-Moe, Is a Shy Blue-Haired Girl with Lonely Doll Girl. In fact, her speaking ability is barely function and has to relied on her magicaldoll to do the talking most of the time. She is so bad at the even subtitle somehow manages to make it's harder to understand what she is trying to say! Though she starts to open up once she meet with the main character who also help her making friends. She still has a very hard time speaking however, fortunately she seem to texting just fine.
The Fairy prince Edgar from the King's Quest series. Justified by the fact he's spent most of his life being "raised" by the cruel and vicious Lolotte, and was transformed into a deformed, ugly, green-skinned hunchback. He can barely make eye contact with Rosella without blushing. He's developed a bit more of a spine in his second appearance, but he's still very shy and quiet.
Paya from The Legend of Zelda: Breath of the Wild gets embarrassed and shy incredibly easily for many reasons. For example, Link standing too close (or within ten feet of her), Link not wearing a shirt, being asked about the birthmark she was named after, the list goes on. It slightly goes away, in that she stops getting embarrassed at some of Link's more benign questions, after Link spends the day protecting her from the Yiga clan after they steal the Shrine Orb out of her and Impa's house, though she will still get flustered at the above instances.
There's Fuuka Yamagishi, the team's resident Mysterious Waif and Mission Control, who has a school reputation for being frail, shy and easily bullied. She's actually much more resilient and headstrong than her reputation suggests, but when Junpei "Casanova Wannabe" Iori points out how developed she looks in a swimsuit, she can only manage a panicked, inarticulate squeak and quickly hides behind the other female party members in embarrassment.
And possibly topping Fuuka is "Justice" social link NPC Chihiro Fushimi, the painfully shy student council treasurer who can't speak to any male character about anything at all without stammering. Completing her social link sidequest helps her get better, and reveals that she's also a (very mild) Type B tsundere. By Persona 4, she's overcome her shyness enough to become Student Council President.
And a third, surprising, example in Persona 3 is Akihiko Sanada. The team's Spirited Competitor and school boxing champion, most of the time he's an Aloof Big Brother sort that most of the girls in the school would love to date ...at least, until he actually tries to impress a girl, and falls into a nervous stammer. A character video late in the game shows him reading books in his room on how to talk to girls and trying, and failing, to rehearse a conversation without getting flustered. This is probably best exemplified by talking to him in Tartarus when playing as a female protagonist in a romance with him. Up to this point, Akihiko has consistently shown the ability to filter out distractions while fighting, even when emotions are running high. But when the female player merely speaks to him then, he's reduced to this: "Wh... What? Oh... sorry... Im... kind of nervous... ...Dont look at me too much."
Persona 4: In the initial start of the story, Yukiko Amagi is highly revered among her classmates and many people of Inaba for her beauty and status, but is uncomfortable whenever someone compliments her looks and doesn't think very highly of herself, feeling worthless. She depends on her childhood best friend Chie Satonaka to stick up for her and fend unwanted guys off who pressure her into going out with them to an extent that it becomes a crutch. As the game progresses and Yukiko obtains her Persona, she begins to gain the strength and self-confidence she needs to stand up for herself more.
Ayane Matsunaga serves as another example of this trope within the game.
There's Jasmine, the Gym Leader of Olivine City, to the point where her gym has no other trainers in it besides herself. She makes a cameo appearance in the fourth generation games and proves to be just as timid as ever. All the more jarring when her Steelix kicks your ass.
The fourth generation also has Marley, who only speaks just enough to get the point across.
Male example in the fifth generation is Cilan. Compared to his anime counterpart, the Cilan in the game comes off as very shy and having almost no confidence in his ability. His tendency to stutter before, during and after the battle doesn't help his case. When you compare his personality to his brothers Chili and Cress, it's very jarring.
In Pokemon Xand Y, Battle Chatelaine Evelyn fits this trope to a T, up to the point that she stutters in her speech.
Same goes to Shizuka Hirose, the main chick from Gakuensai no Oujisama, though this depends heavily on which male she's shipped with: she's more shy to some guys, but more open to others.
Satura from Runbow turns out to be this in the DLC mission. She may have ultimately become friends with the Hues and Vals after her defeat in the normal adventure mode, but she still feels shy and lacks confidence around them due to her being born without color, preferring to sit by herself in The Last Luau and draw in her sketchbook. It's only after she gets convinced to join the others on a trip to the new Outta This World poster that showed up that she starts to get over it.
Annie from Splatoon is a shy and fidgety shop owner. Luckily she has a loud, Jerkass partner in Moe.
Despite her being quite a tough girl, Sonic the Hedgehog's Blaze the Cat does have her moments of this, especially around the more bubby Amy Rose, ever so cheerful Cream, cocky Sonic, or even Peach and Daisy.
When around girls, Knuckles can qualify for a male version of this, especially when taking quotes like this into account.
Rouge: Still, you were pretty dashing and daring this time around.
They cover their faces with masks and wear robes that cover their entire bodies... clearly, Shy Guys are the kings of this trope.
Also the Boos, who will stalk and haunt Mario as he attempts to go about his adventures, preparing to rip him apart with their razor-sharp fangs.... but can't do it if he's looking at them.
Despinis, one of the Homunculus of Duminuss in Super Robot Wars Reversal fits this trope to a T. Even when attacking, there's not a chance she'll not slip up the phrase "I'm sorry". All with a face of a half-sick, super shy paedophile bait. On the bright side, she does have some sort of kindness streak and this proves to be beneficial that in OG Gaiden, instead of dying like in her original role in R, she ends up surviving.
Emil from Tales of Symphonia: Dawn of the New World fits this trope squarely. It probably doesn't help that everyone else in his hometown, his own aunt and uncle included, believe he's a worthless scum who'd be better off dead. Emil also subverts this trope in Ratatosk Mode, where he becomes a very blunt Jerk with a Heart of Gold, and the exact opposite of the "Normal" Emil.
Elise from Tales of Xillia. It's a result of the people in her town treating her like a freak because of her abnormal proficiency with magic for her age, on top of seldom being let out of her home by her caretaker for safety reasons.
Mio Kisaragi, Megumi Mikihara and Miharu Tatebayashi from the first Tokimeki Memorial. Each, in their own ways: Mio is a MeganekkoIll Girl, Megumi is very sheltered and naive, Miharu is clumsy and awkward.
Nitori Kawashiro from the game Mountain of Faith. Her first reaction to the player character? To run away.
Kisume from Subterranean Animism hides in a bucket out of shyness. She is so shy, most of the time she often outright refuses to show her face to people. The implication being that the head that peeks up from the bucket is not hers... And, yea, in case you're wondering; her being an Ax-CrazyShrinking Violetis canon.
Lammy from Um Jammer Lammy is a very shy, insecure girl. She appears utterly uncomfortable with talking to people with whom she isn't already acquainted, and she becomes stricken with anxiety when put on the spot or made the center of attention. Further evidence toward this comes in when she flashes back to her and her band making the poster for their upcoming gig, specifically saying, "My picture doesn't have to stand out."However, when she has her guitar, either with her orin her mind...
Oka Ruto, the Occult Club president. Her default walk cycle has her hunched over and trying to take up as little space as possible, and she speaks in a halting, hesitating manner. Her student info also notes her shyness.
Ayano "Yandere-chan" Aishi acts like this if she gets too close to Senpai (in fact she switches to the same walk cycle as Oka). The hand-wringing can be something of an inconvenience, as she drops whatever she was holding (like, say, a bloody knife).