tailor your application?

I’m putting this out as a separate question to avoid hijacking the ask a scatterbrain thread about cvs.  I advise students to try to tailor their cover letter and cv to any job they really want, to make it sound like they know something about that specific department, especially if that job is at a non-PhD department, and have said that I think mailing mass-produced materials to dozens of jobs you don’t really want is probably a waste of effort.   But I base this opinion on relatively little data.   So that’s my question, to folks on either side of the hiring process in non-PhD departments.   In hiring, do you attend to whether the materials are tailored to  your department versus being obviously generic?  On the job-getting end, did you tailor your application materials?  Also, on both ends, how often was there a personal connection through the advisor that facilitated the job-getting, rather than the paper application package?