ISPs themselves often uplink into further ISPs. But with a fatter pipe at some kind of bulk cost.
I guess you could lease a T1 from the local phone company (Verizon here) and hook up to a backbone provider. I can't remember the name of the one we used here a few years back, but they were the way to go at one point. (Not for ordinary customers)
Completely not worthwhile, of course, especially with FiOS going around nowadays.
(of course, none of this gets you hooked up any more "direct" to "THE" Internet, because that presupposes the existence of a monolithic entity)