There are at least three big ones (BMI, ASCAP, and SESAC) -
I'd love to know, how popular or well-known are the PROs in the US?
I don't know how how "well known" they are - probably not known much at all. Most Americans that I've talked with don't understand or think about copyright law, which is not surprising, since the United States' copyright laws are almost contradictory in what they allow and disallow, and there's alot of undefined grey.
I only know about the PROs because I was casually curious about copyright issues for church services, after seeing copyright claims on a few projected song lyrics during a service. Apparently worship teams can't play (modern) music in churches unless the church pays the annual licensing fee to one of the organizations.
Though, looking here (CCLI is not one of the big three - I guess it sub-licenses, or else contracts its own musicians?), the prices seems quite reasonable - and though I roll my eyes at the ironic humor of the situation, at the same time I understand the whole artist-wants-to-be-paid-for-his-work thing, which is very similar to the software piracy issue.