I would also like to add that an attitude and aptitude to continue learning and expanding your current GIS skills is a must....not just what you know right now. GIS software and capabilities are constantly changing, and although the basics such as understanding coordinate systems, etc. are VERY important, realizing what you've learned in school isn't the end product, but just a base to build upon, (I think) is also important. There are plenty of free or low cost training opportunities, in there aren't new skills to learn at work....
....and in this same tone...don't think you know everything about GIS just because you have a degree/cert/GISP/experience. In my opinion, nobody knows everything about GIS (although there are many that know a lot about some facets of GIS). And if you do think you know everything (or your attitude is such) I would have second thoughts about you. (this kind of plays into the team player concept)
btw - This is for those positions that I consider full-time GIS jobs, vs. the -ologist and just about every other type of job that just need the minimum to be able to do some analysis and produce maps. Although continuing education is important in just about any field, I wouldn't expect occasional GIS users to put in that much effort to become experts.
Disclaimer...I only have one employee (but support many), and they have worked for me for about a decade. Prior to that, I went thru several new hires, fresh out of school but, in my opinion, they liked the bright and shiny of GIS concept, and never had their heart into wanting to do GIS. None of those stuck around very long (<2 years). Being able see who will fit is sometimes as hard getting a job....and can be just as stressful.
EDIT: ..rather than adding another post, editing this to comment about Cole's cover letter question. Keep in mind my relatively small hiring sample..but including other GIS staff hires. In our Department, we do not use a HR to filter applicants for jobs like this, and instead we tend to analyze, choose and hire the applicants ourselves....based on criteria from the job class, policies, etc. So for me, the cover letter is a summary and I read it, but I'm looking more at the resume showing actual training and experience when "scoring" the application for interviews. Of course, if/when I look for a job, I would probably include one. Better to have it and have it set aside then not include it and have it be a requirement.