Inscrutable Oriental

Japan: So inscrutable that he can't even *smile*.

Throughout the years, people from the far East have been depicted in Western media as being not quite as willing to visually express their emotions compared to their peers. This stereotype derives essentially from the attitudes of Western colonialists who, unwilling or unable to learn the social conventions of "natives" or treat them as equals, simply wrote them off as inscrutable.

If treated positively, a character who follows this trope can come across as being a calm, cool, and fairly collected (if a bit eccentric) person who may also serve as a source of wisdom and encouragement. If treated negatively, characters come across as being overly dour, uptight, dull, and all around boring fellows who seem to have trouble comprehending concepts like leisure or fun.

This can be shown tropewise as being The Stoic in more serious and/or positive portrayals. And as The Comically Serious or Only Sane Man in more comedic and negative portrayals. The Old Master may also be this trope.

All in all, this trope can be described as the Eastern counterpart to Germanic Depressives. Any kernel of truth in the stereotype can be attributed to the one universal social mannerism throughout East and Southeast Asia, and which British people would understand: Don't make a fuss.

Contrast Asian Rudeness.

Examples of Inscrutable Oriental include:

Anime and Manga

Japan from Axis Powers Hetalia, pictured above, who is extremely popular in his country's fandom due to the self-deprecating stereotypes he embodies. His memorized rules of conduct consist of gems like agreeing to consider options when he actually means 'no', never giving straight answers in a corner, becoming more polite when he is annoyed by other people, and apologizing when others are causing trouble.
- Hong Kong seems to be this way too, being depicted in his Drama CD appearance as a Deadpan Snarker Emotionless Boy.
Taki from Maiden Rose, although done rather interestingly so that he has his defrosting moments while at a foreign military academy and then suddenly switches to "inscrutable" mode upon returning home, only to confuse the hell out of Klaus who goes with him.

Comics

The new Judomaster's first appearance in Justice Society of America is characterized by her being silent, cold and reserved out of combat. Mind you, before then, she'd been portrayed as witty and perfectly capable of speaking English, but these things happen. Mind you, she did warm up a bit when she fell for Damage.
Mocked in a strip of the italian comic Sturmtruppen where a crossdressing spy is ordered to escort the japanese ally to another base, and affirms that "Nothing can surprise these inscrutable orientals". Cue to the japanese ally trying to hump him.

Spy: Hey, does he know the meaning of "disguise?"
Sergeant: Who knows, he's inscrutable...

Film

Mr. Miyagi from The Karate Kid.
Parodied with a line from the western comedy The Great Bank Robbery, something along the lines of: "You sure are inscrutable, Fong. Just like all you Secret Service fellas."
Seraph and the Keymaker from The Matrix films were meant to invoke this trope, fulfilling the "Orientalist fantasy".
Subverted in the Harold & Kumar Go to White Castle movies: Harold's coworkers think he is this, but for the viewers, he's The Everyman with a weed habit. Culminates in a spectacular World of Cardboard Speech in which Harold spells out to his coworkers how very goddamned much he is not this, thank you.
Spoofed in Around the World in Eighty Days, where Fogg asks for help from a stereotypical looking old Chinese man in loud pidgin English. The man turns out to speak English perfectly.

Literature

Shiro and Ancient Mai from The Dresden Files.
A Tree Grows in Brooklyn features a Chinese Launderer character who's stereotypical in other ways, but it actually calls out this trope. The young heroine sees the Chinese man as a wise mystic and assumes he's listening thoughtfully when she talks to him, when in reality he doesn't speak English and is just waiting for her to leave.
In The Westing Game, Mrs. Hoo is seen this way at first, but it soon becomes obvious that it's solely a language barrier.

Live Action TV

Señor Chang, the Stereotype Flip Spanish teacher in Community, rants about this.
Kaito Nakamura from Heroes.
Agent Kimball Cho on The Mentalist is the deadest of the deadpan snarkers and most definitely The Stoic. However, he's also willing to go Cowboy Cop and Not So Stoic when the situation calls for it.
Averted on FlashForward, in which John Cho played the more Hot-Blooded, emotional and temper-prone half of a pair of FBI partners. In fact, John Cho has pretty much made a career out of averting this stereotype (see Harold & Kumar Go to White Castle, above).
In season 2 of The Mole, Dorothy was so withdrawn and emotionless that many other contestants suspected her of being the Mole. It turns out she wasn't; she deliberately invoked this trope to draw contestants' suspicions toward her and away from the true Mole so that they would flunk on the quiz about the Mole and be eliminated. It worked well enough for her to win in the end.

Tabletop Games

Lampshaded in the description of Lacquered Tablet, an Agatean ambassador described in GURPS Discworld Also:

Someone once told him that the rest of the world sees Agateans as inscrutable, and he decided this was a good idea. He is very inscrutable, and goes everywhere with a gang of large guards chosen for their inscrutability.

Web Comics

Your Mileage May Vary on the ethnicity of {...} from Hanna Is Not a Boy's Name: he has almond-shaped eyes (more noticeable when they're not surrounded with black stuff) and black hair, and apparently has a sentimental attachment to paper cranes. And he's decidedly The Stoic, commenting that he's been told he's "hard to read", and basically fits the entire personality component of this trope. So he might be this, or he might not. Or maybe being dead leaves you a little detached from emotional ups and downs. It's hard to say.

Western Animation

Lampshaded on an episode of Star Trek: The Animated Series, during an exchange between Kirk and Sulu. Incidentally, this episode was written by Walter Koenig, who played Chekov on TOS and was friends with George Takei in real life:

Kirk: Any chance of teaching me that body throw? Could come in handy sometime.
Sulu: I don't know, sir. It isn't just physical, you know. You have to be... inscrutable.
Kirk: Inscrutable? ... Sulu, you're the most scrutable man I know.

Video Games

Shen Yu in Evil Genius is described as "inscrutable", which is not surprising as he's a take on Fu Manchu.