When I was a law student at Yale, I initially did not put my LSAT score on my resume. However, as a first-year student, with all our grades pass/fail first semester, it quickly became apparent that the students who went to Yale, Harvard, Amherst and similarly prestigious schools for undergrad were getting Summer law firm jobs, and those of us who went to Brandeis, Trinity, Binghamton, etc.--schools with lesser brand names--were not. In other words, law firms seemed to be using undergraduate institution as the best available proxy for ability. Seeing that, and wanting to prove I was "no slouch", I put my LSAT on my resume. I probably wouldn't have done this if Yale had class rank or other objective measures of student performance, but, frankly, it seemed to help.
I also remember that when I was clerking, I interviewed a clerkship candidate who attended a good regional law school, and was at the top of her class. Did it influence me that her resume said "LSAT: 48" (the highest score at the time)? Yes, it did. My judge didn't normally hire from this law school, and I didn't know much about the quality of students or instruction there, but her LSAT score showed that she could have attended Harvard, had she so desired. That said, I'm sure some recruiters, especially those who did well in law school but did not have stellar LSATs, get offended when they see an LSAT score on a resume.
UPDATE: See also this post, discussing the trend of employers asking adult workers about their SAT scores from long ago.