In a broad sense, Java is pretty similar to C. I think if you wanted a perspective-altering experience, learn something like Lisp or Haskell. But I agree that there is value in learning C. You should probably learn both C, and Lisp or Haskell or Scheme or whatever functional-ish language looks interesting.
(This is with the assumed goal of getting an overview of programming language styles. If you have specific application-building demands, then language choice may be more dictated by that, e.g., Objective-C for iOS.)
After at least 1-2years I would suggest that you start learning Lisp, then Elixir http://elixir-lang.org/
If you thought becoming a programmer is easy, everybody can do that, you're right, but becoming a good programmer is NOT. You have to learn the scientific background, if you want to understand things and not just use what get. For that matter I would recommend reading SICP.
Well, let's say you don't want to become a good programmer, but just make money, then go and learn ABAP, Cobol, ADA or JavaEE. (Just beware that some Pro C guy, could make you jobless one day, by writing a LLVM back-end that converts existing code to LLVM bytecode and then to C.
There are many people who have the same question, I would recommend @pg to propose a FAQ containing info about it.
That's the best advice I can give you currently, but if you know somebody who can give you better advice, then please let me know about it too. Because what doI know, nothing, everybody can benefit from your and other people's experiences.
C++/C# looks like the thing you want. The other answers are STILL valid though. Depends on what platform you want to develop for. C# is windows only (don't argue with mono).
People reading this having the same question should give us this info next time:
Age: Kid,Jr,Senior
Experience:
What you want to achieve: Desktop,Mobile,Web
Platform support: iOS, Android, Windows, Linux, OSX, HP-UX, ...I recommend learning C after Java. It's much more difficult to learn, but your prior Java experience will help you pull through.
Note: this all depends on what you mean by "some" programming experience.