Every programming language I have ever seen has been based on the Latin alphabet, this is not surprising considering I live in Canada... But it only really makes sense that there would be programming languages based on other alphabets, or else bright computer scientists across the world would have to learn a new alphabet to go on in the field. I know for a fact that people in countries dominated by other alphabets develop languages based off the Latin alphabet (eg. Ruby from Japan), but just how common is it for programming languages to be based off of other alphabets like Arabic, or Cyrillic, or even writing systems which are not alphabetic but rather logographic in nature such as Japanese Kanji? Also are any of these languages in active widespread use, or are they mainly used as teaching tools? This is something that has bugged me since I started programming, and I have never run across someone who could think of a real answer.
Many languages allow Unicode identifiers. It's part of standard Java, and both g++ (though you have to use \uNNNN escapes) and MSVC++ allow them (see also this question) And some allow using #define (or maybe better) to rename control structures.
But in reality, people don't do this for the most part. See past questions such as Language of variable names?, Should all code be written in English?, etc.
APL is probably the most widely known. It even has a cool keyboard overlay (or was it a special keyboard you had to buy?):
In the non-alphabetic category, we also have programming languages like LabVIEW, which is mostly graphical. (You can label objects, and you can still do string manipulation, so there's some textual content.) LabVIEW has been used in data acquisition and automation for years, but gained a bit of popularity when it became the default platform for Lego Mindstorms.
Well, there's always APL. That has its own UNICODE characters, and I believe it used to require a special keyboard too.
There's a list on Wikipedia. I don't think any of them is really prevalent though. Many programmers can learn to write programs with english keywords even if they didn't understand the language. Ruby is a good example, you'll still see Japanese identifiers and comments in some Ruby code.
Other people are answering with languages that use punctuation marks in addition to Latin letters. I wonder why no one mentioned digits 0 to 9 as well.
In some languages, and in some implementations of some languages, programmers can use a wide range of characters in identifiers, such as Arabic or Chinese characters. This doesn't mean that the language relies on them though.
In most languages, programmers can use a wide range of characters in string literals (in quotation marks) and in comments. Again this doesn't mean that the language relies on them.
In every programming language that I've seen, the language does rely on punctuation marks and digits. So this answers your question but not in the way you expect.
Now let's try to find something meaningful. Is there a programming language where keywords are chosen from non-Latin alphabets? I would guess not, except maybe for joke languages. What would be the point of inventing a programming language that makes it impossible for some programmers to even input a program?
EDIT: My guess is wrong. Besides APL's usage of various invented punctuation marks, it does depend on a few Greek keywords, where each keyword is one letter long, such as the letter rho.
There'is one langauge used in russian ERP system called after company, which developed it 1C. But it's identifiers and operators has english analogs.
Also, I know that haskell has unicode identifiers support, so you can write programs in any alphabet. But this is not useful (My native language is russian). It's quite enough that you have to type program messages and helpful comments in native alphabet.
I just found an interesting wiki for "esoteric programming languages".
Well, Brainf* uses no latin characters, if you'll pardon the language...and the pun.
Agda.
Sample Snippet:
mutual
data ωChain : Set where
_∷_,_ : ∀ (x : carrier) (xω : ∞ ωChain) (p : x ≼ xω) → ωChain
head : ωChain → carrier
head (x ∷ _ , _) = x
_≼_ : carrier → ∞ ωChain → Set
x ≼ xω = x ≤ head (♭ xω)