A job listing says that they don't want any phone calls, emails, faxes, etc. Is there any other way to make you stand out as an applicant after submitting your application?

I agree with Jeremy. I had successfully helped a friend land a job at a research institute here in the Triangle by using resources like Jigsaw - a  mostly free database of companies/contacts. If you are good at writing respectful, concise introduction letters, then use resources like Jigsaw to arrive at the best guess as to who the requestor of the headcount is (and I DON'T mean the HR hiring manager. They will just shut you down). In this case, it was a biomedical research position, and the candidate had me look for the "Principle Investigators" most likely associated with the project. The introduction letter should clearly convey your proficiency/experience with the elements of the program they are looking to address by hiring a candidate. The introduction letter should be to the point and honest, and believe it or not, you might not even mention the open position, but rather discuss your offerings in the context of any open opportunities within your program/group/team/ etc. the goal here is to have it appear as an honest prospecting letter sent in by someone who: has done their research is competent in their field that it may be a coincidence there just happens to be a job posting ex: “Dear Dr. So-and-so: I understand your team might be expanding your drug discovery research lab, in the area of (be as specific as possible)”. The hiring manager should be able to get the unwritten message that you are respectfully simplifying the whole system by going direct, because there is a chance you are the best qualified and it won’t be a waste of 15 minutes on the phone to find out. The research institute in the above example immediately contacted my friend back, and ultimately hired her. The key to success here was: don’t be out looking for any old job because you are desperate. Be genuinely qualified, and be ready to deep-dive at a moments notice. Being in sales, I do this for cold calling and have found myself answering an inbound call from a VP seconds after sending an introduction email (which is ALWAYS a rush)! You are not “closing” for a job offer at this point, you are just “closing” for a call back, so: KEEP IT BRIEF with a few concise sentences wherein you can bullet no more then 3 strengths that you KNOW are crucial to the program in question. the letter (with your best resume) was send by US mail, and I will say it again - it was short, short, short. the organization has a simple structure; the Principle Investigator was, with 98% certainty, THE guy staffing the project. You may need to do a little more research with larger, multi-layer companies. Good luck, I got a free dinner out of it!

I'd work around that.  There is no stipulation that you can't tap your professional network to get your materials in front of the hiring manager.