It depends what program you're applying for.
I started e-mailing professors around the same time I was sending off applications to let them know that my application would be coming in and they should take a look at it.
You need to do a certain amount of work before you e-mail professors, at least at the graduate level, because you need to be somewhat familiar with their research work. I read through a lot of papers by a lot of professors and then e-mailed them saying something like:
Hi Prof. X,
I'm an instructor teaching psychology at University Y in Lahore, Pakistan, and have greatly admired the work you've been doing on Topics A, B, and C. I'm currently applying for the PhD program at your University Z, and I hope that you will consider me a potential graduate student given that my research interests overlap substantially with yours.
[Insert some basic ideas for what sort of work you could see yourself doing with said professor]
Finally, I'm wondering if you can share a draft of your currently unpublished paper [blah blah blah]. I would really appreciate your help, and look forward to hearing more about your work.
Yours sincerely,
Future Student.
Professors *love* e-mailing their papers to students, so go to the faculty webpages for your prospective supervisor and go through their list of publications and ask them to send you a PDF of some of them -- that's a nice way to begin an e-mail conversation with them, and they're pretty friendly and helpful once you demonstrate your interest in a genuine manner.
E-mailing professors beforehand is a really, really good idea, because if you sound smart via e-mail, they will be sure to look up your application and give it a fair chance.
