I did when looking for jobs. Your resume has all your skills, experience, etc but I always tried to customize my cover letter to try to show how my skills, experiences, would benefit the company I was applying to.
For example, I applied for a web developer type job so I emphasized my web developing skills in the cover letter. Another job was a computer engineer working on embedded systems so I tried to emphasize my skills in that area in my cover letter for that application. My resume really doesn't change though.