This is the workhorse stitch in beading. Flat peyote is a great stitch for geometric design and also often serves as a foundation of embellishment. Peyote in the round is used in bezeling and shaped designs.  This stitch has some flexibility because there is only one pass of thread through each bead. For greater stability consider using brick stitch.

Because of its stability and "shapability" brick stitch is often used for dimensional beaded items where peyote won't be stable enough. It's often used for earrings because brick stitch can be formed into geometric shapes such as triangles, circles, chevrons and ovals. 

This stitch is worked in essentially the same manner as single brick but two beads are picked up for each stitch. It is very shapable but tends to have a more elongated appearance then single brick stitch.  

This tubular stitch is great for making long strands of beads and is often used in necklaces and delicate bracelets. It's a tubular ladder that sets the beads on top of each other, squared in aspect with a sight tilt, rather than in a spiral. It's quite flexible, which makes it great for necklaces, and can be used for purse handles as well.