Uses: back-up knot, and stopper knot
This knot is so basic you probably grew up being able to tie it, and you just called it “a knot”.
This knot has two major uses. First, a lot of people use it as a back-up for their harness tie-in. This has the added adavantage of ensuring the free piece of the rope does not hit you in the eye. Second, it is smart to tie this at the end of your rope before rappelling, so you do not rappel off your rope. (Which happens.)
Uses: joining two ends of rope, creating a loop
Most generally, the double fisherman is used to connect two ends of cord or rope. Most commonly, people use this knot to create a loop of cord for anchor building.
Uses: attaching yourself to the anchor, building anchors, attaching things to the center of the rope
When leading a climb, you can use the clove hitch to quickly tie into an anchor. Or you can use it to help equalize an anchor. Definitely learn to tie the clove hitch with one hand.
Uses: attaching a loop to things, building anchors
When you get lucky, you can use a tree as part of your anchor. Trees make bomber anchors, and they are faster than building one from gear. Just toss some webbing around the trunk, and finish off with a girth hitch. Done. On rare occassion, people also use this knot to connect a sling to their rope.
Uses: friction knot to attach a cord to a rope, auto-blocking rappel and belay, ascending rope
You will need to know how to tie a Prusik if you ever want to rappel from a climb. Rappelling is the absolute most basic self-rescue technique for rock climbers, and often the only way down from a multi-pitch climb. One Prusik can serve as an auto-block while rappelling, two can help you ascend rope in a pinch.
Uses: belaying without a belay device
If you drop your belay device, you can use the munter hitch to belay your partner. This is an extremely valuable skill to have in your toolbox. Learn to tie it with one hand.
Uses: isolating bad sections of rope, attaching yourself to the anchor
The Alpine Butterfly loop is a great way to create a little loop in your rope. And the loop will not come undone if you pull on the rope in either direction. If your rope gets worn or has a core break, you can use this knot to isolate the offending section of rope. This also takes less rope than a figure-8-on-a-bight.
Uses: Escaping the belay, passing a knot on rappel, self-rescue
The munter-mule is a favorite knot to escape a belay. That is, if you are belaying and the climber is stopped for a long time or you need to do something, how do you let go of the rope without dropping your partner? Tie a munter mule into the rope and then clip a biner into the loop. Bam. Now your hands are free to do whatever.
The real benefit of the munter-mule is that it allows for a smooth transition back to belaying. Just undo the loop and you have your normal munter hitch.
As an added bonus, you can use the munter-mule to pass a knot on rappel. For instance, if your rope has a core break, and you protect that with a butterfly knot, you can still rappel.
Am I missing your favorite knot? Or have I forgotten to mention something important about one of the knots above? Leave your thoughts in the comments below.