It depends on exactly what you want to do, and as stated above it's the CS concepts that matter, not the specific language. That being said, there are a few things that are nice to have in your toolbox:
1. A fast language for simulations and large calculations such as C/C++.
2. A good scripting language. Perl and ruby are personal favorites.
3. (optional) A good symbolic math language. R was mentioned, and I have to agree with that. It's becoming much more widely used, and some of the packages are pretty good. Other options are matlab and mathematica.
4. While not quite a programming language, learn how to use databases and how to design good databases to hold the information you want to hold and do the processing that you're interested in. From my experience, one of the biggest problem in bioinformatics right now is the huge number of hard-to-use file formats. It's gotten to be ridiculous, and scientists seem to keep reinventing the wheel here. Databases really aren't that hard to use, they've been optimized extensively, and they're more robust than any simple file system could ever hope to be.
Also not quite programming, but I'd recommend becoming familiar with the linux environment. It's free, and it's gotten to be very user friendly. In addition, all of the tools I mentioned above are available and free for linux. Ubuntu is a good distribution, but there are other options available.
My personal toolbox includes:
-Ubuntu with mysql, rails (a web server) and emacs (a programmer-specific text editor)
-Code::Blocks for C/C++ development using gcc as a compiler
-Perl for quick tasks / data analysis, etc.
-ruby for when perl is a little too sloppy and I'd like a bit more structure but don't want to spend hours writing it in C++.
-R for mathematical and statistical data analysis
Obviously I do this quite a bit, so you might want to start out in a simpler setting. Perl will probably give you the most bang for your buck, and ruby can teach you a reasonable amount about object-oriented programming and structure. C++ is insanely powerful but requires a significant time commitment to become proficient in.