When job seekers sign on with a search firm in order to be represented and marketed to job opportunities, few of them truly understand the implications to them in terms of which if opportunities they will be exposed to, and which organizations they will be limited to. As a recruiting leader, I can tell you that I have had to pass over some excellent, highly qualified candidates because they've been submitted by search agencies. When a company isn't accepting referrals from agencies, agencies either don't make referrals (because they won't earn a placement fee) or they submit referrals that are 'unsolicited'. When I receive an unsolicited referral, I have two choices: pursue the candidate and if I hire the candidate, fight over not paying the referral fee in court, since I didn't sign an agreement and shouldn't be bound to the referral fee terms, or, pass over the candidate because it's just not worth the hassle.
In truth, if you're a candidate and have enlisted an agency to help you find your next opportunity, I may not be able to hire you EVER, if your agency has sent your resume to me. Not for the job they submitted you for, not the for job they didn't submit you for, not for the job you applied directly to my company for... Once referred by an agency, you will forever have that agency's fee agreement hanging over your candidacy. You can bet that agencies are shopping the best candidates around to the companies that they think will pay their fee. In fact, I often receive phone calls and emails from agents who say, "I have this excellent candidate who wants to work for your company..." I have to wonder, 'why didn't they just apply, then? If I accept their resume from this agency, I have to pay a fee for them. If they apply, I can hire them for free! Shucks, I may as well look at all the folks who have already applied and are free...I'll call this agency back if I can't find a great candidate through my own efforts.'
My advice to you is this: unless you really, really have no idea how to look for a job, or absolutely must conduct your job search in complete secrecy...you don't need an agency. Just talk to people you trust, ask to be referred to positions by friends and others in your personal/professional network, and apply for the positions you're a great fit for using a great resume that demonstrates how you have performed well in roles that have prepared you for those you're applying for.