We had a thread on this awhile back, might want to do a search.
Really it depends on your research area. I defintely need at least a moderate level of understanding of computer programming for my research, as well as hardware/circuits since I frequently end up dismantling computers to replace parts, will be rewiring things in the future, etc. Learn to love Matlab if you're doing EEG/ERP research.
Obviously you need to Word/Excel/Powerpoint (maybe Access too if your lab uses it). That goes without saying, but those are all absurdly easy to use. You'll likely need to know more stats packages than SPSS since it simply isn't capable of everything by itself (Amos for SEM/CFA, any of a number of bundles for IRT, etc.)
Any of these would be helpful, though whether or not any are expected is way to dependent on your individual research line for us to answer.