14-gauge is a good size for strong clasps, bangle bracelets, and substantial links for chain.
16-gauge is also good for clasps and bangles and heavy rings or links.
18-gauge can be used for clasps, but you must work harden the wire when you're finished so they're strong enough to hold their shape. It's also good for head pins for some beads (none with tiny holes, though). It's good for wire wrapping and making jump rings. Sometimes you may make ear wires from 18-gauge, but some people can't wear that thickness in their ears.
20-gauge is perfect for ear wires. Some people may also buy 21-gauge for ear wires, but it's a bit harder to source. 20-gauge is also good for head pins, eye pins and jump rings.
22-gauge is a good size for head pins and eye pins for small beads, and for wire wrapped loops.
24-gauge is perfect for Viking knit, and wire weaving. And for making wrapped loop links with beads.
26-gauge can be used for finer Viking knit, and for crocheting and wire weaving. And for head pins for very small-holed beads.
28-gauge is great for wire crochet and wire weaving.