Actually, Sauron did not help/make any of the rings, but the one. He persuaded the elves to make the ones for the dwarves and men, then tainted the finished ones with his power to bend them to his will. So really, he only MADE one, but tainted his power with 17.
Sauron directly helped create sixteen of the nineteen rings, all of which were given to Elves until he put on the One Ring and they perceived his intentions. Three were crafted alone by Celebrimbor and became the greatest of the nineteen. Sauron was unable to recover them like he did the other sixteen. These sixteen were the rings that he gave to the Dwarves and Men who would more easily fall to his power. The Elven rings were kept secret and safe, but their power faded when the One Ring was destroyed, though they were never corrupted like the other sixteen because Sauron had no hand in their creation.