My favorite are box clasps made with vintage buttons or intaglios. Box clasps are two-piece clasps that open when you push down on the exterior lever of a wedge-shaped piece of metal (tongue), compressing it so that it slides out of the opening. Push it back in the groove and it clicks into place.
I also love to use toggle clasps. One section of the clasp is formed into a circle or other shape with an open center. The other half is a thick bar that attaches to the components at the other end. When you insert the "T" into the circle extends past the circle's edges to hold the jewelry in place.