Russian – Vladmir Nabokov describes it best: “No single word in English renders all the shades of toska. At its deepest and most painful, it is a sensation of great spiritual anguish, often without any specific cause. At less morbid levels it is a dull ache of the soul, a longing with nothing to long for, a sick pining, a vague restlessness, mental throes, yearning. In particular cases it may be the desire for somebody of something specific, nostalgia, love-sickness. At the lowest level it grades into ennui, boredom.”
Yagan (indigenous language of Tierra del Fuego) – “the wordless, yet meaningful look shared by two people who both desire to initiate something but are both reluctant to start”
Indonesian – “A joke so poorly told and so unfunny that one cannot help but laugh”
Inuit – “To go outside to check if anyone is coming.”
Czech – Milan Kundera, author of The Unbearable Lightness of Being, remarked that “As for the meaning of this word, I have looked in vain in other languages for an equivalent, though I find it difficult to imagine how anyone can understand the human soul without it.” The closest definition is a state of agony and torment created by the sudden sight of one’s own misery.
Japanese – “A mother who relentlessly pushes her children toward academic achievement”
Scottish – The act of hestitating while introducing someone because you’ve forgotten their name.
Tshiluba (Southwest Congo) – A word famous for its untranslatability, most professional translators pinpoint it as the stature of a person “who is ready to forgive and forget any first abuse, tolerate it the second time, but never forgive nor tolerate on the third offense.”
Czech – This word means to call a mobile phone and let it ring once so that the other person will call back, saving the first caller money. In Spanish, the phrase for this is “Dar un toque,” or, “To give a touch.”
Brazilian Portuguese – “The act of tenderly running one’s fingers through someone’s hair.”
German – Quite famous for its meaning that somehow other languages neglected to recognize, this refers to the feeling of pleasure derived by seeing another’s misfortune. I guess “America’s Funniest Moments of Schadenfreude” just didn’t have the same ring to it.
German – Translated literally, this word means “gate-closing panic,” but its contextual meaning refers to “the fear of diminishing opportunities as one ages.” (Altalang.com)
Japanese – Much has been written on this Japanese concept, but in a sentence, one might be able to understand it as “a way of living that focuses on finding beauty within the imperfections of life and accepting peacefully the natural cycle of growth and decay.” (Altalang.com)
French – The feeling that comes from not being in one’s home country.
Pascuense (Easter Island) – Hopefully this isn’t a word you’d need often: “the act of taking objects one desires from the house of a friend by gradually borrowing all of them.”
Danish – Its “literal” translation into English gives connotations of a warm, friendly, cozy demeanor, but it’s unlikely that these words truly capture the essence of a hyggelig; it’s likely something that must be experienced to be known. I think of good friends, cold beer, and a warm fire.
L’appel du vide
French – “The call of the void” is this French expression’s literal translation, but more significantly it’s used to describe the instinctive urge to jump from high places.
Arabic – Both morbid and beautiful at once, this incantatory word means “You bury me,” a declaration of one’s hope that they’ll die before another person because of how difficult it would be to live without them.
Spanish – While originally used to describe a mythical, spritelike entity that possesses humans and creates the feeling of awe of one’s surroundings in nature, its meaning has transitioned into referring to “the mysterious power that a work of art has to deeply move a person.” There’s actually a nightclub in the town of La Linea de la Concepcion, where I teach, named after this word.
Portuguese – One of the most beautiful of all words, translatable or not, this word “refers to the feeling of longing for something or someone that you love and which is lost.” Fado music, a type of mournful singing, relates to saudade.
14 Comments • Options • Oct 22, 2010
Christopher Lin, English, motherfucker! I speak it!
24 votes by Andrew Brown, Chelsea Henry, Alex Kamil, (more)
My favourite is the Yaghan word mamihlapinatapai, which describes “a look shared by two people with each wishing that the other will initiate something that they both desire but which neither one wants to start.” It is listed as the most succinct word by the Guinness Book of World Records as of 1993.
Options • Sep 21, 2010
Joshua Levy, Curmudgeon
17 votes by Xianhang Zhang, Gary Valan, Shannon Larson, (more)
A few famous ones from Europe with cultural importance:
Danish hygge (coziness or tranquility) 
Dutch gezellig (cozy, fun, quaint, can connote belonging) 
Swedish lagom (“just the right amount”) 
Portuguese saudade (deep or nostalgic yearning) 
German Weltschmerz (“world-pain”, a kind of world-weariness) 
It’s interesting that many of these are to some extent identified with a country’s (perceived) national character.
Of course, this just scratches the surface of a big topic [6,7].
Comment • Options • Sep 10, 2010
16 votes by Joshua Levy, Richard Henry, Kevin Der, (more)
Meraki (Greek) – Doing something with soul, creativity, or love.
Waldeinsamkeit (German) – The feeling of being alone in a forest.
Pochemuchka (Russian) – A person who asks a lot of questions.
Esprit de l’escalier (French) – A witty remark that occurs to you too late, literally on the way down the stairs.
Chantepleurer (French) – Singing and crying at the same time.
7 Comments • Options • Sep 10, 2010
Andrew Cheung, I work at GroupMe.
10 votes by Seb Paquet, Yishan Wong, June Lin, (more)
My favorite is Fingerspitzengefühl.
It translates roughly to having a good feel for the situation at hand and being able to react accordingly.
Often attributed to Erwin Rommel’s tactical ability.
Also, baydin, which means “foretelling the future through magic” in Burmese.
6 Comments • Options • Oct 23, 2010
Antone Johnson, Lawyer, exec, advisor to lean startup…
6 votes by Gary Valan, Dimitry Lukashov, Richard Henry, (more)
Hebrew: Dayenu – “it would have been enough for us” (sung at Passover)
French: Lots of mountaineering and skiing-related words and phrases (après ski, arête, couloir, crevasse, gendarme, moraine, pied à plat, piste, serac). One family that comes to mind is the multiple words for “ice” in different contexts, whereas we really only have one in English: glace, glaçon, glaciaire, glacé, glacier, glacial, verglas.
Italian: sotto voce – intentionally lowering one’s voice for emphasis; sprezzatura, the art of effortless mastery (one of my favorites — aspirational); mammismo – the cultural phenomenon involving a belief among young men that no one can love them as much as their mothers.
Scores (pun intended) of musical terms in Italian also don’t have direct English equivalents. Many of them have been borrowed into common English usage as nouns or adjectives (piano, opera, orchestra, virtuoso, prima donna) or are commonly understood among music fans (a cappella, aria, arpeggio, coda, concerto, legato, libretto, soprano, staccato) — but some have more esoteric, precise meanings that are tough to describe in English without resorting to illustrative examples or lengthy, detailed descriptions (allargando, cadenza, coda, coloratura, divisi, rubato, acciaccatura, appogiatura).
German: Dülfersitz – in mountaineering, a kind of rappelling that involves straddling a fixed rope and wrapping it around the body to descend without any special gear.
Spanish: estar – the verb “to be” in a temporary sense (for example, to be tired or hungry, or to be located somewhere) vs. ser , “to be” in a permanent sense (male, tall, blond); bien educado sounds like “well-educated” but really means to have been raised well, with good values, and to be a good person
Comment • Options • Sep 10, 2010
Patrick Vlaskovits, “Vell, Zaphod’s just zis guy, you know?”
7 votes by Richard Price, Gary Valan, S. Alex Smith, (more)
Schadenfreude (German) which means deriving pleasure from the misery of others. The closest English language equivalent would be “glee”.