It depends on the orientation you want for your career but here are a few tips:

• Matlab (for data analysis and modeling. Used much more than Maple or Mathematica by engineers)
• Python (general purpose scripting language, easy to learn with lots of libraries for computing and modeling, SciPy, NumPy, etc)
• C/C++ (for some scientific application development).In many small/medium size companies, the biomedical engineer needs to integrate it's code into the code base himself. In that case, you at least need intermediate knowledge of the main application language which is often C++ (in order not to do stupid things to the application code).

Of course, my suggestions are more oriented toward the algorithmic biomedical engineer (2D/3D imaging, bio-signal processing, etc). If you are more into the mechanical or bio-material domain, you probably don't need to be as knowledgeable in computer programming.

Regards

It depends on the orientation you want for your career but here are a few tips:

• Matlab (for data analysis and modeling. Used much more than Maple or Mathematica by engineers)
• Python (general purpose scripting language, easy to learn with lots of libraries for computing and modeling, SciPy, NumPy, etc)
• C/C++ (for some scientific application development).In many small/medium size companies, the biomedical engineer needs to integrate it's code into the code base himself. In that case, you at least need intermediate knowledge of the main application language which is often C++ (in order not to do stupid things to the application code).

Of course, my suggestions are more oriented toward the algorithmic biomedical engineer (2D/3D imaging, bio-signal processing, etc). If you are more into the mechanical or bio-material domain, you probably don't need to be as knowledgeable in computer programming.

Regards

To add to Bruno's answer

Definitely Matlab - which will give you an understanding of Python, Octave and Stata.

C/C++ are an advantage but not compulsory. You may also want to dabble in Perl. 

However, Understanding a good statistical language/programme/software is key and is often lacking in the engineering disciplines - by this i mean a good grasp of using SPSS or Minitab. 

For a UG biomedical engineer, the following programming languages are required;

MatLab, C/C++, Octave, SPSS, StatGraphics. Other simulation sofwares like LabView, Proteaus, NI software etc., maybe be helpful  depending on the branch of biomedical engineering you deal with.

Having a fair knowledge on statistical softwares and simulation softwares in addition to the programming softwares will be of a great advantage.

With an emphasis on medical devices and other product development these days, learning about embedded controllers and being able to program in C/C++ is a necessity. For the same reasons Matlab is essential to modeling, providing a simple GUI, and  as a diagnostic interface to your project. It will be much easier obtaining a job or entering graduate school with this knowledge.

If you are planning a lot of data acquisition then LabView from NI may be worth learning.

I concur with the other software mentioned already.