Other than having stellar credentials and packaging yourself well in a resume and cover letter, there really aren't too many options out there these days to ensure your candidacy for a job really gets the attention you want it to. I agree with you that employers are probably seeing more and more applicants for fewer and fewer jobs, so the real question becomes, after you've done all the preparation and packaging of yourself for employers, how can you be sure that they will even spend the time necessary to see that you are qualified for the job. I think the best way to get in front of the people doing the hiring and firing is to follow-up after submitting an application and to also try and find jobs that are not posted on the popular public job boards like Craigslist and Monster.
A good place to look is
www.Hound.com This job site cuts the competition for you. It only posts jobs from employer webpages that have never been posted on public job boards. They do all the work for you and put all these less competitive jobs in one place. Basically, Hound lets you apply to the jobs that not everyone and their mother and brother are also applying to.