The obvious answer is NONE, when compared to modern cars, but there are cars that handled well for their time. Tires were crap (comparatively), but even the lowly Corvair, (Ralph Nader notwithstanding) could handle a twisty road with aplomb. As could Shelby Cobras. And Shelby GT-350s. Depends on whether we're just talking American cars in the 60s, American Muscle Cars, Pony Cars or Sports Cars. Hell the GT-40 and the Daytona Coupe both won LeMans, beating Ferrari I think.