How important are citations when applying for jobs or promotions?
In my experience, citation counts are considerably less important than recommendation letters, but they still matter, especially for tenure.  For fresh PhDs, high citation counts are definitely helpful, but they're not a hiring requirement for most fields in CS.  But for tenure, it's really hard to build a successful case without at least one high-impact (post-thesis) publication.

Smart committees know to gather citation counts, publication counts, acceptance rates, impact factors, h-indices, and other quasi-objective numerical data from reasonable sources and to compare them with peers in the applicant's field.  (For my promotion cases, for example, my citation counts were mined from Google Scholar, not ISI, and I was compared against other theoretical computer scientists, not other computational-geometers-who-play-with-surface-graphs.)  Alas, not every committee is smart.