Learn something of a completely different paradigm than the usual — i.e. procedural, for example C and Basic, or you'd be just wasting your time, IMHO. From the top of my head, the forerunners of their own paradigm are the next — for all, there are decent, free implementations:

• functional, prefix: Lisp or Scheme (see the many recommendations in this thread)
• Object: Smalltalk (for example Squeak)
• Postfix, stack based: FORTH
• Logic: Prolog (SWI-Prolog)
• Somewhat related: expert systems (event triggered), for example CLIPS

As a nice generic language, which feels a bit like a descendant from both Smalltalk and Lisp, but with a more procedural-like syntax, take a look at Python.

I can also recommend to take a look at Dr. Dobbs' Journal, which every year brings out a normal issue around alternative programming languages, and occasionally, a dedicated special issue.