50% according to this article. They mention 80% in 1860.
I'm not 100% sure of the source there but I have heard similar numbers around 50%. Think of all the self-employed people doing jobs that just don't exist today in the US - delivering milk, fruit, fish, newspapers, door-to-door salesmen, and that's on top of jobs that still exist today with a lot of self-employed people like AC repair, plumbing, etc...