Let $R$ be a ring. Then we know that a free module over $R$ is projective. Moreover, if $R$ is a principal ideal domain then a module over $R$ is free if and only if it is projective or if $R$ is local then a projective module is free.
We also have a very big question on free properties of projectives module over a polynomial ring, that was Serre's conjecture, and now is Quillen-Suslin's theorem.
I wonder, do we have a general condition for a ring $R$ so that every projective $R$-module is free which involves all of the cases mentioned above ?