What are important languages to learn to understand different approaches and concepts?
When all you have is a pair of bolt cutters and a bottle of vodka, everything looks like the lock on the door of Wolf Blitzer's boathouse. (Replace that with a hammer and a nail if you don't read xkcd)
I currently program Clojure, Python, Java and PHP, so I am familiar with the C and LISP syntax as well as the whitespace thing. I know imperative, functional, immutable, OOP and a couple type systems and other things. Now I want more!
What are languages that take a different approach and would be useful for either practical tool choosing or theoretical understanding?
I don't feel like learning another functional language(Haskell) or another imperative OOP language(Ruby), nor do I want to practice impractical fun languages like Brainfuck.
One very interesting thing I found myself are monoiconic stack based languages like Factor.
Only when I feel I understand most concepts and have answers to all my questions, I want to start thinking about my own toy language to contain all my personal preferences.
Answer
Matters of practicality are highly subjective, so I will simply say that learning different language paradigms will only serve to make you a better programmer. What is more practical than that?
Functional, Haskell - I know you said that you didn't want to, but you should really really reconsider. You've gotten some functional exposure with Clojure and even Python, but you've not experienced it to its fullest without Haskell. If you're really against Haskell then good compromises are either ML or OCaml.
Declarative, Datalog - Many people would recommend Prolog in this slot, but I think Datalog is a cleaner example of a declarative language.
Array, J - I've only just discovered J, but I find it to be a stunning language. It will twist your mind into a pretzel. You will thank J for that.
Stack, Factor/Forth - Factor is very powerful and I plan to dig into it ASAP. Forth is the grand-daddy of the Stack languages, and as an added bonus it's simple to implement yourself. There is something to be said about learning through implementation.
Dataflow, Oz - I think the influence of Oz is on the upswing and will only continue to grow in the future.
Prototype-based, JavaScript / Io / Self - Self is the grand-daddy and highly influential on every prototype-based language. This is not the same as class-based OOP and shouldn't be treated as such. Many people come to a prototype language and create an ad-hoc class system, but if your goal is to expand your mind, then I think that is a mistake. Use the language to its full capacity. Read Organizing Programs without Classes for ideas.
Expert System, CLIPS - I always recommend this. If you know Prolog then you will likely have the upper-hand in getting up to speed, but it's a very different language.
Frink - Frink is a general purpose language, but it's famous for its system of unit conversions. I find this language to be very inspiring in its unrelenting drive to be the best at what it does. Plus... it's really fun!
Functional+Optional Types, Qi - You say you've experience with some type systems, but do you have experience with "skinnable* type systems? No one has... but they should. Qi is like Lisp in many ways, but its type system will blow your mind.
Actors+Fault-tolerance, Erlang - Erlang's process model gets a lot of the buzz, but its fault-tolerance and hot-code-swapping mechanisms are game-changing. You will not learn much about FP that you wouldn't learn with Clojure, but its FT features will make you wonder why more languages can't seem to get this right.
Enjoy!