What is the equivalent of “Say cheese!” in other languages; that is, expressions used to naturally display the teeth work of the person you are about to take a picture of?
In Spain, we were told that “patata” was the go to expression.
Others?
In Poland person taking photo usually just says uśmiech!, which means simply ‘smile!’. We don’t really have some standard expression we are supposed to say to expose teeth when posing to photo.
I was told that in Latin America that “Whiskey!” is the equivalent, no idea why or how widespread this actually is (or just a something use by english speaking tourists).
Patata would not yield a smile but more of a pucker.
My father in law never picked up on this concept. He thought saying cheese was just to make your face less frozen. So he would have all his children say “stinky feet” instead. Needless to say, they all had the final “t” tongue action on their faces in every single picture.
In Mandarin, it’s ‘shu qiezi’ — literally, “Say ‘eggplant’.” Confusing, until you realize that the mouth position for the syllable ‘qie’ basically requires you to smile.
In Japan all the schoolgirls say “Piiiisu!” and give the peace sign. I don’t know why.
In Mexico, “whiskey” is definitely used.
In Korean it’s “kimcheeeeee!” (of course).
I don’t know why either, but isn’t “piiisu” a direct japanization (or whatever you call it) of the english word “peace”?
Yep, I’m pretty sure it’s just a borrowing of “Peace”. IANA Japanese Photographer, but the most common thing I’ve heard Japanese people use is “Ichi tatsu ichi wa?”, which just means “One plus one is…?”, to which most people enthusiastically respond “Niiii!” (Twooooo) while the surfers tend to go with a sarcastic “San deshou, bokeyaro” (“Three, dumbass!”).
For what it’s worth I hear hai, chiiiizu quite often also. (You probably guessed, but it comes out as “okay, cheese!”)
Refugee
That’s pretty common, especially among men. Incidently, saying piiisu has gained popularity in the last 20 years.
My Taiwanese wife says they say seven qi (pronounced “chi”) and Chinese say eggplant qiezi (pronounced which a chi sound.
Swedish: Säg omelett! (“Say omelette.”)
But you don’t say patata as if you’re asking your mother for more potatoes. You actually make a face, paaaah-taaaaaah-¡taaaaaaaaaaaa! and if the photographer still hasn’t taken the picture by then, you stay with your face frozen (and melting slowly), looking more or less like this but not so green: 
If you’re in a Hilton hotel, you say “Hilton Stilton.” 
I’ve never encountered any similar expression in Thai, so I asked the wife. She says there is none.
Minor nitpick, Mandarin for “say” is “Shuo”, but if they’re talking entirely too fast (as they tend to), then it could be missed.
In German, either you’re just told “bitte lächeln” (smile, please) or, in some cases, you’ll also be told to say “cheese”. Yes, in English. No idea why.
It’s standard in Panama too.
What, no “tequila”? 