Computers & IT (Non-Engg)

General Software
1) Familiarity with different operating systems (Windows, Mac, Linus, Unix, etc.)
2)Microsoft Office and document processing (Word, Excel, Powerpoint) since as engineers we have to be able to communicate our work to others.
3)Matlabis a common programming tool used for engineers, although C+ and Fortran has it's applications as well. I.e. I know CFD codes use Fortran a lot since it compiles code it executes large data sets much quicker.
4)CAD Software. The most common are Solidworks, Unigraphics, ProEngineer, Catia, AutoCad, and there are many others. If you create things, CAD is a necessity. Different companies have preferences on CAD software however file compatibility is continuously improving.
Experiments
5)National Instruments LabVIEWis a standard for experimentalists these days. It allows easy interfacing between hardware and software so that you can acquire data, control experiments, and process/analyze data. It is graphical based programming (which I find very intuitive and easy to learn).
Computations
6)FLUENT, OpenFOAM, ANSYS,etc. Depending on what you are working on and if you have access to commercial software. Here is a good list of software for FEAList of finite element software packages
Graduate Student
7) Latex. This is an open source document processing software which has a steep learning curve but once learned, it makes writing a thesis or dissertation much easier and higher quality. LaTeX - A document preparation system or LaTeX
You will undoubtedly learn many specialized software packages throughout your career, especially since software is inundating every aspect of our lives and work these days. For example, I have also learned video editing software, specialized software for processing data acquired with a specialized measurement tool (Davis - for processing PIV data), web programming software (html and CSS), and more.
Let your education and career guide you, but always keep an open mind to learning new software, you'll be surprised at when certain skills come in handy!