Contacting potential advisers before deadlines
It is definitely helpful to contact potential advisers for many reasons.  In my experience, one important reason is that a professor for whom you would like to work may not have space or funding for you.  Sometimes those things can be overcome, and sometimes they can't.  If there is only one professor whose research interests you in a given department, and that professor isn't taking students for some reason, that could make your decision for you.  It's not a pleasant situation, but I have seen it happen several times.

You might also find that, after talking to a potential adviser, the focus in their research isn't quite what you thought it was.  Of course you can find that out by reading the recent publications, but a conversation can also be enlightening.  They might tell you about one or two specific projects you would likely be working on, and if those projects don't interest you, you might want to move on.

If things look like they could work out, it is still an excellent idea to stay in touch.  If someone on the admissions committee gets to know you somehow, that will really set your application apart.  The chair of the graduate admissions committee at my undergraduate institution even told me that, more than once, he has admitted a student simply because he or she was calling or emailing and expressing real interest and desire to become a student in the department.  Don't be annoying, but a couple of emails and/or a phone call or two never hurt anyone.

If there are several potential advisers in one department, that is great.  It likely means that department focuses on research that interests you.  Don't be afraid of getting in touch with more than one professor.  The more people that recognize your name, the better.  Just be sure to be polite and respectful and leave a good impression.

Good luck!