genejockey 

I use Simple Green, but I don't soak for longer than a few minutes and then I rinse with a large excess of hot water and lay parts out to dry on newspaper. Mineral spirits will do a great job, too, but the room I do my bike work in is poorly ventilated.

BTW, most solutions used by professional watchmakers for cleaning watch parts have a base of mineral spirits. In watchmaking, you need all the parts to be absolutely, molecularly clean before you reassemble and lubricate, because unlike bikes, watches only run right if there's a tiny, tiny amount of lubricant only in just the right places, which stays in place because 1) the oils are formulated not to spread and 2) the scrupulous cleaning doesn't provide an 'escape route' for the oil. By contrast, with bikes we want oils that will penetrate the rollers of the chain, or the pivots of brakes and derailleurs.

Oh, and speaking of gasoline, the Army's 1945 Technical Manual on watch repair suggests gasoline as a solvent for cleaning watches! I imagine during WWII, gasoline was easier to come by than watch cleaning solutions!