Depends so much on the celeb. Some of the biggest ones in the world (the real A-listers) go about their everyday business without fuss and no one bothers them.
I think as a rule of thumb those who don't court attention away from their work usually are treated with respect and not intruded upon.
I suppose when you think about it the real celebs aren't papped much; i.e. Streep, Depp, Mirren etc. They get photographed at events and such but you rarely see anything of them leaving restaurants, grocery shopping etc.