Is it okay to mention Stack Overflow reputation points in my resume?

It's absolutely a reasonable thing to do. Keep in mind though that a lot of people won't know what a certain StackOverflow reputation means, so it's useful if you can make it meaningful somehow. This could be done with a percentile ("top .01% of active users").

There is no such thing as "OK to mention in my resume". Everything is OK as long as it is true and makes me -- or someone else reading the resume -- wish to talk to you in person. I remember one amazing engineer having "a capella chorus in a foreign language". Seemed to have worked well for him. :-)

I think it's perfectly fine to mention the reputation points in your resume. It's not bragging as Anon User mentioned, but it's yet another achievement which you earned. As you have said that you have fairly good reputation, this would testify your skills which you mentioned in the resume. But again, I would like to say if most of the reputation came from answering questions (rather than asking good questions), only then should you include it in your resume, which I think is pretty obvious.

I could see it either way, but you should definitely reference your profile so they can read up on your programming Q&A and see what kind of programmer you are.

It purely depends on who you are sending the resume to. If the interviewer happens to be a guy who has no clue what Stack Overflow is, you are wasting realestate..

Yeah. I mentioned StackOverflow on my resume and it got noticed—and remembered—positively. I figure anything that stands out like that can only help. To people familiar with the site, it demonstrates that you are helpful and know how to communicate clearly. And most people unfamiliar with the site will just ignore that point on your resume or ask you about it (which gives you a great chance to explain why it's relevant and how it matters). I can't imagine many scenarios where it would go against you. It helps to give context. A raw reputation score by itself is not particularly meaningful, especially to someone less familiar with the site. Giving a percentile or tying it to specific technologies (top X in some tag) are both reasonable options.

For academic jobs, some ideas: http://academia.stackexchange.com/q/61749/452