Hood-liners - (from the late 1930s onward) have been manufactured with automotive hood liners constructed from asbestos fibers. I have heard this many times but have never found actual proof its true.
Brakes - asbestos brake linings
Clutches - Some clutch parts in use today, both in new and older car models, contain asbestos.
Gasket Material, Heat Seals, Valve Rings and Packing - For decades, asbestos-containing gaskets, heat seal material, valve rings, and packing were used in virtually every system that involved the transport of fluids or gases.
Lots of aftermarket parts especially from other countries still contain asbestos.