A similar question could be asked for human languages.
My rant done, let me produce my list:
* Ancient Greek (or Latin) - inflectional: Just sheer coolness of it and the literature you can read in the original is enough. But these languages are the grand daddies of Indo-European (unless you wanna go Hittite or Lithuanian) grammar and will teach you valuable linguistic and conceptual points (i.e. cases, noun declension). Learning this is like learning ALGOL, kind of useless but you'll see where a lot of concepts have originated from.
* Mandarin (i.e. Chinese) - isolating: Two points: Seeing the syntaxlessness of these languages is mind boggling and expanding experience. Many poet/translators have remarked about the "timelessness" of Chinese poetry, because verbs don't have tense markings. And, of course, the writing system is very interesting, too. Like learning Lisp (Scheme), an interesting, expanding experience.
* Turkish - agglutinative: (Disclaimer, I'm a native speaker) A great into to the agglutinative aspect of languages (unless you want to learn an American-Indian language) and an interesting phonetic system, so regular, is used as an example a lot in phonology courses.
* Swahili: The concept of noun classes (a generalization of grammatical gender) is bewildering when you first encounter it, swahili has 16 of them (http://en.wikipedia.org/wiki/Swahili_language#Noun_classes)
And more esoteric ones that would be great to learn: My favorites would be Basque (interesting language isolate) and Georgian.
To your list I would add Finnish or Hungarian for some hard-core agglutinative features. I don't speak Turkish, so I cannot tell to what extent it behaves similarly in this regard. See for example this list with 2253 forms of the word "shop" in Finnish: :) http://www.ling.helsinki.fi/~fkarlsso/genkau2.html
Then to cover some indoeuropean vocabulary, I would add one slavic, one germanic and one neolatin language for good measure, although this is a bit too eu-centric.
For some examples of what I mean by concepts that are sometimes difficult to translate, look at most examples on this blog: www.betterthanenglish.com/
The older examples are generally better, and I don't agree with the phrase "untranslatable word", but it should provide some general idea of the kinds of ambiguities that would be lost in translation.
You might get a scowl, or some other non-verbal feedback, during speech.
You can't translate poetry. Sure, you can find the equivalent words between the language in which the poem has been written and the language you want to translate into, but the original meaning is lost. I can give you countless examples, but the easiest it would be for you to pick a poems' book written in a foreign language (I assume you already know a foreign language) and read it in original. And then read the translation in your native tongue. They aren't quite the same, are they?
I'll also add Chinese's rather powerful "de" statement. It can be possessively and descriptively, but you'll often see whole sentences jammed up before a "de" in order to describe a single noun (or wildly recursive uses of "de"). About half the time I'm at a loss to translate sometime I find that I'm just not using "de" enough.
You can achieve the same effect in spoken English by speaking the jammed up portion quicker, and it's sometimes written with hyphens: "a (whole-sentence-jammed-up-before-a-de)-before-it noun."
I suppose it's a lot like the Blub Paradox. It's not that you can't do that sort of thing in English, it's just more painful.
German as a second language was mandatory for all elementary pupils in fourth, fifth, and sixth grade in my childhood school district, very unusual for the United States. I had more German in junior high and senior high (in two different states) and then Russian in senior high. I entered university as a Russian major and immediately began taking Chinese, switching my major to Chinese as I grew in delight for that language. I have had formal instruction as an adult in Modern Standard Chinese (a.k.a. Mandarin), Cantonese, Biblical Hebrew, Literary Chinese, Attic Greek, Biblical Hebrew, Japanese (first in the medium of Chinese, then in English), Taiwanese, and Hakka, and various courses in linguistics (also in the mediums of both English and Chinese). I have engaged in self-study of Biblical Aramaic, Mongolian, Spanish, French, Latin, Hungarian, Malay-Indonesian, Esperanto, Interlingua, etc., etc., etc.
I have to respectfully disagree with the strong version of the linguistic relativity hypothesis. Within each language grouping, people differ far more in their personal thinking along the dimension of visual thinker or not, or auditory thinker or not, than people differ from one another in thought patterns based on language background. But it is useful to learn another language and to live in another culture for exposure to new basic assumptions, and the same applies to learning computer language paradigms. Besides the book mentioned in another reply, I like the books
http://www.amazon.com/Programming-Language-Pragmatics-Third-...
http://www.amazon.com/Essentials-Programming-Languages-Danie...
too as overviews of various programming languages.
I've studied Spanish (in highschool) and Japanese (for years) and while there were some new concepts (in grammar and sentence structure, mainly) they don't apply to anything but languages. And I'm not likely to try creating a language, and I've never had trouble expressing myself in the one I have.
What's the english word for 'schadenfreude'? or 'entrepreneur'?
After edit: the saying cherished by linguists in English is "'loanword' is a calque, and 'calque' is a loanword," which I find helpful for remembering which word is which.
That's a great line! I never heard it before.
Its not exactly uncommon for people to own businesses and to then employ people to run the company for them. This is pretty much how most long established public companies work.
Some governments actually try to restrict the usage of loan words and try to keep the language 'pure'. I think this is death for a language, and I'm glad English adopts new words so readily.
Someone recently told me that they thought that almost all the really interesting creative works were in English these days because English is so expressive, where many other languages have only 1 word for a thing. The language he used as a reference was Spanish, which he is fluent in. The word he used as an example was 'garbage'. He said in Spanish he had only ever used 1 word for it, but in English we have 'trash', 'junk', 'refuse', 'waste', etc, etc.
I don't know if that's really why, but it's an interesting thought.
The words 'trash', 'junk', 'refuse', 'waste' all carry different connotations. Be forewarned, my information is largely relative to Wisconsin. Other regions of the US may use the words differently.
If applied to a person: trash usually refers to someone that's disreputable in some grievous way, waste would refer to some that squandered some talent or resources. Junk wouldn't usually apply to a person but junkie means a drug addict. Applying refuse to a person would be silly, but probably be .
If applied to stuff that's thrown out: Trash is a generic term for anything that's thrown away. Waste is usually consider excess like banana peels. (waste and trash are largely interchangeable in conversation, the distinction isn't usually important) Junk would refer to material possessions that are no longer wanted like an old couch. No one would call banana peels junk. Refuse is a pretentious/higher class term for trash used by rich old ladies.
I don't believe refuse is in the common usage any more. I've never heard it used outside of Star Trek 6 and some older movies. It's meaning is similar to "trash" but it can also refer a place where trash is stored.
Most of english is this way. Words are extremely flexible and can be used in a variety of ways with many meanings. Context is extremely important. I'm not sure how other languages work, I only speak english.
In general, verbs in Spanish are way more expressive than in English: http://en.wikipedia.org/wiki/Spanish_verbs