Stretch Magic, Elonga, Gossamer Floss & Elastic Cording from Rings & Things, plus crimp tubes specially designed for use with stretchy cording. In many cases, no needle is required. String beads directly onto the cord, or use the Igolochkoy needle/threader or Beadalon's Elastic Cord Needle.
What's the difference between these types of stretch cord?
Stretch Magic is super clear (or opaque black), and available in 0.5mm, 0.7mm, and 1mm diameters. It knots well, and easily stretches to twice its original length. Can be crimped instead of knotted!
Elonga and Gossamer Floss are SUPER STRETCHY shimmery multi-strand beading threads from 0.3mm to 1.0mm, and are easy to knot. All sizes are excellent for bracelets. Double the cord for extra strength, and add a drop of superglue for extra hold.
Classic elastic cord is popular for a wide variety of crafts and strung jewelry. It is strong and opaque.