The figure eight is the most secure and common way to tie into your harness. The knot is almost idiot-proof, all you have to do is add an extra twist to a normal knot then follow the rope back through. The knot is the strongest if the working end stays on the inside and no strands are crossed. This can also be tied very easily when making a loop. The figure-eight can be untied with ease after it has held weight.
The Bow line looks simple but it is hard to learn and easy to screw up when tired. The Bowline is a safe tie-in when the free end is tied off. If not, the line will pull through. The bowline is easy to adjust and can be used to tie in to multiple anchor points and to equalize the load on each point. A bowline on a coil can also be used to tie into the rope without a harness.
The Prusik has many uses since it can perform two functions and it is easy to do. A sling can be used to create a Prusik knot. The Prusik can be used as a self belay during a rappel as well as securing a fallen leader. The Prusik can slide along a rope when loose but tightens when weight is placed on it. The sling has to be twisted around the main line twice then looped back through the original loop.
The Klemheist is a variation on the Prusik. The Klemheist is easier to tie but not to pronounce. The Klemheist also works with a webbing sling.
The Hedden is a ratchet knot just like the Prusik but used with webbing. It is quick and easy to tie since it is a variation on the figure-eight but used like a Prusik.
The water knot is used to make a webbing sling.Do not use this knot to make a rope sling. Make an overhand knot and follow it back through from the other side. Leave at least an inch of tail in the ends.