Computing for Psychologists has a great post on Computing skills for (psychology) students, most of which I think applies to ALL graduate students and faculty (whether full time or adjunct).  With the exception of the section on Experimental software (which is specific to psychology – your field likely has it’s own), I can’t imagine building an adequate career at this point in history without knowing most of these skills.

I would suggest two additions to the list.

1. The Statistical/Mathematical group should include qualitative research tools, like NVivo or Atlas.ti.  Just as most intro stats courses also introduce a stats tool like SPSS, I think most qualitative classes should introduce a qualitative tool and that we should all have at least basic skills with both.  We may not all DO both types of research, but knowing a bit about the tools available can help us when we collaborate with others.
2. The centrality of a good reference management software and the importance of backups are listed under Miscellaneous.  I’ve posted on both of these topics before many times, and believe they are FAR to important to your success as a scholar to throw at the bottom of any list.  So consider this a way of raising their profile.

Take a good look at the entire list.  The academic job market is a tough one, and we can no longer compete if we are not competent with technology.  This list will give you a good starting point.