Munter Hitch
Not really a knot, but actually a moving belay hitch, essential if you drop your belay device. I include it here because of its close relationship to the clove hitch.
Prusik
This and the following friction knot are made from a thinner cord or sling wrapped around a thicker rope. When tensioned, they grab onto the line and are useful in a variety of situations. They are, however, fairly fickle: The knots could slip if you don't put on enough wraps, and any slippage could result in heat, melting the thin cord. In general, knots like the prusik hold better when the cord is thinner and suppler and when the rope is thicker, softer, and fuzzier.
The knot doesn't work well with webbing. It needs 6-mm or 7-mm cord to hold well on a 10-mm to 11-mm rope.
The prusik needs three wraps on a single rope and two wraps on a doubled rope (as in a rappel). Make sure that the knot is cleanly tied; any mess here will greatly reduce its holding power.
Kleimheist
This is the preferred knot when your only material is flat webbing. Tied with 11/16-inch nylon webbing, the knots hold pretty well. With Spectra slings, the slipperiest of all, the knot needs at least five full wraps to be sure. The knot is hard to loosen after loading, and when it starts to grab, it binds up quite a bitan irritation but not a danger to the rappeller who is using it as a backup.