No. Do you believe that by paying money your privacy is guaranteed? Even Fastmail's privacy is doubtful regarding its non-US clients -which would be my case if i used it.

Paying for it allows them to spend time researching better systems and gives them some buffer in the dace of legal attack. See also anon.pennet http://en.wikipedia.org/wiki/Penet_remailer

Ok, but why would anyone set up and run an extremely privacy-hardened service for you, for free?

What would a company possibly have to gain by creating a service that a lot of people will use and not pay for?

Despite what you may have "learned" from the examples of Facebook and Twitter, companies giving away things for free isn't a very good business model.