Dramatic Stutter

Characters in some works, particularly Japanese works, tend to stutter whenever even slightly surprised.

(Alice, Bob's wife, returns home early, without going shopping) Bob: A... Alice! You're early!

Can also be written as "A-Alice! You're early."

Probably happens due to Rule of Perception applied to surprise. Deteriorates Into Gibberish can also come into play to demonstrate cases of extreme nervousness.

Examples:

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Anime & Manga

My Hero Academia: Protagonist Izuku Midoriya starts out as a Shrinking Violet who tends to stutter when he's nervous, excited, or startled. This habit gradually phases out over time as he gains more confidence, though it still pops up from time to time.

Asian Animation

Occurs in episode 61 of Pleasant Goat and Big Big Wolf. Wolffy can sing Magic Music to turn himself into paper and move however he wants. However, when the goats surprise Wolffy outside, he stutters and can't manage to sing the song. This give Jonie the opportunity to punch Wolffy.

Films — Animation

In Turning Red, in the astral realm, a younger version of Ming repeatedly stutters the word "I" as she explains to Mei why she is crying.

Literature

Lauchlan of Mix Beer With Liquor And You Will Get Sicker commonly speaks with a stutter. However, this is justified as he's characterized as an extremely anxious and neurotic character. When he's angry or attempting to be serious he can usually repress it, but it takes some concentration.
In Isaac Asimov's robot novels, Elijah Baley dramatically stutters Daneel's name in the first and second books. In The Caves of Steel, the stutter stems from Baley's initial discomfort in talking to a humanoid robot and calling it by the familiar name, but in The Naked Sun, his "D-Daneel" is pure surprise and pleasure at seeing Daneel again.

Live-Action TV

The girl who played Miranda on Lizzie McGuire did this in what seemed like every other line.
Gaius Baltar does this constantly on Battlestar Galactica. Unusual in that he's the only character who does so.

Theatre

Romantic duet of Papageno and Papagena closer to the end of The Magic Flute even called usually just "Pa- pa- pa-".

Video Games

Almost everyone in the Ace Attorney series does this at one point or another.
Happens to most of the characters in Danganronpa at least once.
Double Homework: Dennis insists that the protagonist has been in his room playing video games the whole time, and he gives ones one of these after being Instantly Proven Wrong.
System Shock: SHODAN resembles a sound card malfunction when it happens to her. It probably is a sound card malfunction. As shown in the second game she's quite capable of not stuttering when pretending to be a human scientist. It's likely she just likes the effect, especially given how intimidating it is.

Webcomics

Tower of God:
Rachel: Wa-Wait a minute! *CRASH* Co-come in, Khun.
Girl Genius: Castle Heterodyne personality in a mechanical humanoid body after "Unstoppable Higgs" kicked it a few times.
Gunnerkrigg Court uses this. In a flashback, the main protagonist's now-deceased mother implies she has fallen in love with quick-witted fox Renard, resulting in his use of this trope before she leaves him hanging with a mischievous smile. Happens again years later when, after returning to the Court, Surma's daughter Antimony says she'd let Renard return to the forest if he wanted (him not being able to escape so long as she didn't allow it, being the only reason he's not trapped in a large cell being tortured) and he repeats this action while telling her not to ask that of him, going on to say that the love he had for Surma, while not what he had once believed it to be, hadn't gone away and muses that someone has to be around to protect Antimony.
In El Goonish Shive, Tony stutters his name when confronted with Grace in Tedd's form without Tedd's glasses to hide Tedd's feminine eyes.
Celina's imp in Imp lapses into this when he's nervous, but other characters stammer on occasion.

Web Original

Real Life