Has anyone ever actually calculated the gravity required for a planet to keep an atmosphere

that would depend to a large extent upon what kind of atmosphere you are refrrring to !

Here's the problem. Mar's is nearly airless because it has no protective Magnetic field to HOLD ON to its atmosphere! The Solar Wind blows it away because its unprotected! The Earth is closer to the sun, but our van Allen belts keep the solar winds from blowing our atmosphere away. This is the reason the first four planets are small and rocky. During the formation of the planets, the solar winds blew away what wasn't used by the planets. The outer Gas Giants have large protective fields (Jupiter's actually reaches all the way to Saturn!)

There is no simple answer to this because it depends on the surface temperature and composition of the planet as well as its gravity. However, i have seen an estimate that in order to hang on to enough oxygen to breathe, 0.7 g are required. I have no idea how this figure was arrived at.

The Martian atmosphere is thought to become denser at some times due to climatic changes.

Titan is very cold and the molecules in its atmosphere are moving quite slowly. Ganymede has a negligible atmosphere, well under a millionth of the density of ours at the surface.