I can say first hand that referrals can be very useful during a job search. Many times when a person is not a perfect match for a role per the resume a strong referral from a recognized colleague in the firm can get that person into the door for interviews. If you know of someone in the company you want to apply to, please reach out to them. Have them send in your resume in addition to your online application.
Now, that we know referrals should be used, how do we find them?
Online Sites: Check out your Facebook page and find out where people work. You just might find out someone you knew from high school or college or any past groups/organizations, might work at the place you are applying to. If you know them well, they might just pass your resume onto HR or be open to them listing them as a referral.
LinkedIn: Similar to other social sites, you can search connections and find out if people you know have worked or currently work at the place you are applying. They could also provide good insight into the company culture (the good and bad).
College: Have any professors that you stay in touch with? You should reach out to them to stay in contact of course, but also keep them in mind when job searching. Just think about the huge network that professors have inside and outside of academia! Many still work or have worked in the corporate world and have connections in various firms.
Family and Friends: Think of the folks closest to you. Now think about the people that they might have in their own networks. Now you're getting it! These folks will know of others who might be able to at least pass along your resume.