I would suggest a few to pick up the basics on. You don't have to be a master, but at least understand the differences and concepts. The list is in order by what I consider most important to least important:
1) C/C++
Specifically, learn the syntax and understand the difference between the two. Be able to write a few simple command line programs and try a bit of GUI. There are many, many different tutorials out there for this.
2) Java or C#
As was mentioned above, you can choose one of the two to get a handle on. Again, you don't need to be a master, but write a few simple programs, and start looking a little more into the GUI aspect.
3) Ruby or Python
Next up is scripting. Both these languages are powerful. Learn the syntax (again; sensing a theme?), and do some data manipulation (strings and files, etc.).
4) Prolog or LISP
This is probably not as important, but I feel these types of languages help to build problem solving skills by forcing you to think differently than you would using a more "classical" language. I would recommend SWI-Prolog as a good starting point here.
5) DirectX or OpenGL
If you get through the basics for the list above, you might have time for something a bit more complex, like the above graphics libraries. I'd recommend, if you've chosen to go the C# route, to do DirectX. There's a decent starter tutorial here: ZophusX. If you want the more os-agnostic OpenGL, the tutorials at NeHe are definitely the way to go.
This gives you a rounded start on different syntax styles, plus moves towards more complex concepts.