Apologies for the blatant cut-n-paste from another
thread on the exact same topic.
The problem with the SCJP, at least when I took it, is that it is mostly a
test of knowledge regarding Java syntax and foundations. The SCJP doesn't make you a programmer, and gives absolutely no measure of what your ability to actually write functional software is.
As such, I doubt your score really matters to anyone. As someone who has a degree in a non-technical field, I have found that having the SCJP was useful during the time when I had little experience. Since then it is nothing more than resume padding though.
Even though I scored fairly high (somewhere over 80%, don't remember exactly) I have never mentioned my score in job interviews. The certificate I received from Sun also made no mention of my score. I think if the interviewer is interested, then by all means share your score. Otherwise I would leave it off resumes. I know if I were evaluating a new prospect, having their score right on their resume would just be an annoyance. It's great they could pass a test that ascertains they understand basic Java concepts, but a high or low score gives absolutely no indication of how good they are going to be.