Everyone who sends out a resume does! Even if the cover letter never "came up" in conversation or wasn't mentioned in an advertisement, it's expected that you will write one.
It is regarded as a sign of laziness (sorry about that) to send out a cover letter that is not tailored to the specific company. In the days before word processors, you could maybe get away with it.
Yes, it adds to the wear and tear of looking for a job! But the good news is: the cover letter gives you another chance to emphasize what you have to contribute to the company or organization. Don't give the person screening the resumes a second to entertain the thought: "But how can this person help US?" Your cover letter will answer that question in your own words. Your resume will also answer that question but in a somewhat more rigid format.
Everyone who sends out a resume does! Even if the cover letter never "came up" in conversation or wasn't mentioned in an advertisement, it's expected that you will write one. 