Which celestial object in the solar system has the fastest tangential velocity at its surface?
Hands down it's Jupiter.  It has both the largest radius and faster rotational velocity of the planets, and smaller objects will not be able to compete with that huge radius.  Jupiter's rotational velocity is approximately 13.4 km/s (with some variation due to wind currents, as it is a gas), which can be determined both from Doppler shifts of reflected sunlight, and also from watching the motion of equatorial cloud features.  Saturn is only 10.9 km/s, as it has a longer rotation period and a smaller radius.  None of the other planets can compete with Jupiter, and smaller objects would need prohibitively short rotation periods to have any chance.  For example, the Earth would need to have a day that was about half an hour long to compete with Jupiter.  Even a molecule that spins millions of times a second would need a size on the order of a cm to compete with Jupiter.