In Persona 3, 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... I’m... kind of nervous... ...Don’t look at me too much."
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.
The Manakete Myrrh in Fire Emblem: The Sacred Stones: she's been sheltered an 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.
Path of Radiance brings us Astrid, 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.
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 Lolicon 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.
In Pokémon 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 and 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.
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.
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.
Tifa is a mild example, usually when it comes to Cloud.
Nitori Kawashiro from the Touhou game Mountain of Faith. Her first reaction to the player character? 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.
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.
Hope Esthiem from Final Fantasy XIII. Early on in the game, he was very cowardly until Vanille helped him come out of his shell. Come Final Fantasy XIII-2, he has become a charismatic leader.