While the language is wonderful I would not use it for production systems today. It is my opinion that the language came to be too early and, as a result, has not seen innovation for decades. It also does not help that the leading APL implementations cost thousands of dollars to license. APL is still being used extensively in financial institutions in Wall Street.
J has been mentioned here a few times. Even though J is the work of APL's creator, Ken Iverson, whom I had the pleasure of meeting at various APL conferences, I consider it an abomination and a huge step backwards. I have a feeling Ken might have sought more commercial appeal by using ASCII characters rather than specialized notation. Ironic because of [1]. However, in making this switch, he created a horrible mutation that anyone can rightly recoil at. The language looks like a random vomiting of ASCII characters on the screen. Sad.
Many have commented on APL on this thread. In most cases it is obvious that these comments come from lack of or limited experience with the language. The power of APL comes from two things: Abstraction and Notation.
Abstraction is very much like objects in OO languages or specialized symbols in mathematics.
Notation --through specialized symbols-- is huge. Ken Iverson's own "Notation as a tool for thought" [1] covers this in far more depth than I could attempt here.
I'll just mention one example: music notation. A page in an orchestral score looks like gibberish to someone unskilled in the art. However, to a skilled professional it reads, well, like music. While I am not at that level, I can read guitar or piano sheet music and imagine, for lack of a better word, the music with reasonable accuracy.
That's what happens with APL if you really know it: You read it like music. Much of the criticism and misguided opinion comes from people who simply don't have this level of proficiency with the language. All other languages allow you to be a pretty decent "hobby" programmer in the sense that you don't have to be able to read it like music and you can still produce and maintain software. APL, for non-trivial work, requires true expertise, not superficial exposure. It rewards you with unparalleled productivity and expressive power. It really is a cool language, but you have to invest the time to learn it and read it like music.
Another way to put it: It's like vim. It's a shit code editor until you invest the time and effort to use it instinctively, to play it like a reasonably skilled musician would play a piano: without having to think about which finger to use to press a certain key to produce the desired tone.
That's APL. It's very different than using C or Java. It requires expertise, time and dedication. And perhaps that's the source of its demise. Today most programmers don't care about diving to those depths. Most want to learn the basics and poke around API and code libraries to get shit done and consider super-simple stuff like pointers confusing and complicated.
BTW, to me Python has a number of APL-like features that make it fun and productive. I really enjoy it.