There are a ton of cool knots, some of which have very specialized applications. Among the knots I use most often are the good, old overhand knot, two half hitches, bowline, trucker's hitch, tautline hitch, figure of eight, clove hitch, sheet bend, larks head hitch (aka cow hitch, girth hitch), and a variety of friction hitches plus a few other knots that are useful if and when it becomes necessary to set up a mechanical drag system.
Truckers hitch is very useful when you wish to apply tension of a line such as tying down a boat or rigging a taut line as a clothes line, or as the ridge line for a tarp. Tautline hitches do not have the holding power of the truckers hitch but make it easier to adjust tension on a taut line. They are useful for guying out tent flies and tarps.
Two half hitches is a quick way to secure the end of a line that will be subjected to tension. However, to be fully secure two half hitches need to be under continuous tension or the knot can untie itself. The girth hitch is a quick an easy way to secure a loop of rope or webbing around a post or tree. The clove hitch is a great way to tie off a painter on your canoe to a tree or post, but has many other applications as well.
The bowline and the figure of eight are the standard non-constricting loop knots. The figure of eight is a bit stronger if you are going to subject it to a great load or trust your life to it when abseiling or climbing. But the bowline is so quick and easy to tie and untie that I prefer it about 95% of the time. It is not all that difficult to become confused tying the bowline however, and there are reports of even expert climbers tying it incorrectly. It is also best backed up with a half hitch around the standing line or a figure of eight stopper knot.
Double fisherman knots (really a bend) are very useful for tying the ends of a grab loop on a canoe together or constructing Prusik loops. Bends are knots that tie two different lines together or the two ends of a loop together. Another very useful bend is the sheet bend which is especially useful for tying lines of different diameters together. It is much better than a square knot for that purpose. A bend I like even better for securing two ropes of any size together is the Zeppelin bend, which is quite easy to untie after being place on load. The colorfully-named European Death Knot is another very easy to tie bend which joins two lines or lengths of webbing. It is more properly called an offset double overhand knot. It is useful because the knot is completely offset to one side of the line which is convenient if you have to run the conjoined line over the edge of a ledge or around a tree, etc. The offset knot will not tend to catch nearly as much as other bends will.
A few other really cool knots that might be worth knowing are the timber hitch, the marlin spike hitch, the sheepshank, the arbor knot, the constrictor hitch, the alpine butterfly, and the Evenk Knot or Siberian timber hitch. The last is a hitch that can be tied to secure a line around a tree or post that can be tied with gloves and untied with a simple pull. It is useful if you are trying to secure a tarp ridge line around a tree as high up as possible at the very extent of your reach where an alternative hitch could be quite difficult to untie.
As for knots and hitches that are useful to essential in swiftwater rescue applications there are many. A few common ones include the figure of eight on a bight (directional figure of eight) which places a loop in the center of a line to which a load can be attached that allows the load to be directed along the axis of the line. The Munter hitch (Italian hitch) is another hitch long used in abseiling which has wide application in swiftwater rescue. For making a loop in a length of webbing for an anchor the water knot (which is basically an overhand follow through bend) is best, although it can be difficult to untie if subjected to heavy load.
If you really want to get down in the weeds, there are a huge variety of friction hitches that have been devised to secure a line or a loop to another line under load in such a way that the friction hitch can be easily released and advanced. These are critical for setting up a mechanical drag system. The old standby is the symmetrical three loop Prusik hitch which still works. The Prusik can be tied as a closed hitch (with a loop) or as an open hitch at the working end of an open line. But climbers and arborists have come up with a huge variety of asymmetrical friction hitches, most of which can only be tied using the open free end of a line or a "split tail" (or eye to eye) Prusik cord or length of webbing. Some of these are the Blake's hitch, Distel, Schwabish, Valdotain tresse, French Prusik (aka autoblock, Valdotain), Michocan (Martin), the Klemheist (best friction hitch for a webbing loop), the Bachman, and a few others. If you are interested in any of this I can send you a link to a good resource.
The symmetrical Prusik hitch is a symmetrical hitch that will grab and hold equally well when loaded in either direction. But for climbing, abseiling, and for a mechanical drag system that usually is not what we want. In those applications you want a hitch that will grab and hold tenaciously when loaded in one direction along the haul line, but release and advance readily in the opposite direction and asymmetrical hitches allow for that.