I'm surprised Doc hasn't beaten me to reply here......
I have done very little climbing work with ropes other than a bit of caving and using a safety line when working at heights. So I'm not an expert here. However I use knots alot with my boating, fishing and trapping activities.
Here's what I might use:
Overhand knot. If the end of the cord is doubled before tying this, it makes a quick loop. The basis of the reef knot.
Clove hitch. Handy, and the basis for the very good 'round turn and two half hitches' which I would use a lot for tying the boat to the wharf etc.
Bowline. Everybody should know this one. I've never had a bowline fail, but I do keep a fairly long tail end in case of slippage. Sometimes I will 'take the rabbit around the tree' in another direction to form the Dutch bowline. This version has the tail poking out away from the eye instead of in to the eye and I like this for some applications...but it isn't necessary to tie it this way at all.
Lineman's Loop or Butterfly Hitch. Good for making an easy-to-untie loop in the middle of a rope. A figure-eight loop is probably just as good for many applications, but I think it may be harder to undo. I don't use this much, but I like it. Don't have my own picture of this, sorry.
Reef knot. Should never be used for joining rope where there'd be a problem if it let go. It is not a reliable knot, but is handy for temporary bindings and package tying etc. Reasonably quick to tie, and reasonably easy to undo. No picture available in my collection.
Zeppelin Bend. The best joining knot I've used for joining similar cords that I want to untie later. Excellent knot, but it takes a bit of thinking about to tie.
Double fisherman's bend. Great joining knot, but very hard to undo at times. I will sometimes use a 'half' double fishermans bend to tie a cord back on to itself when I want a neat way of fastening a lanyard to something.
Buntline hitch. I used the slipped version of this to tie my marker flags to trees when I'm trapping. It is one of the best 'slip knots' I've ever used for ease of untying and reliability when tied. You have to be sure that the tail sits in the right place as you tighten this, otherwise when you undo it the rope will have an extra twist and take a little longer to undo. (I sent Doc a picture of this wonderful slip knot that I imagined that I might have come up with all by myself. He sent me back a picture entitled 'buntline hitch' which was identical :foot: And then I seemed to recall that he was the one that had told me about this knot a year or two ago...and I remembered the name from my younger days...possibly when I'd been in Sea Scouts). Good knot, no matter who invented it.
Timber hitch. For fastening the non-looped end of my bowstring, or for towing logs with the crawler tractor. Easy to undo and holds well if the tension is constant
The cow hitch is a simple knot worth knowing. I use a bit of cord around a possums tail in a cow hitch knot to pull the skin from the tail. No pic.
Prusik Loop. These loops will tighten and hold on another rope. Good for climbing a vertical rope, but you'd need two loops to do the job comfortably...one holds your weight while you slide the other up. See a climbing site to see how to use these (and similar) ascending knots
I use other knots too for fishing and a multitude of little jobs. For instance, the Ashley Constrictor knot is a good one, based on a clove hitch, for really binding things together. I've used it as Ashley suggests....as a hose clamp.
Gotta go and organise dinner. I might post more later if it occurs to me. I imagine Doc (Mr Knots himself) will come along sooner or later and provide more good stuff.
D) when you'll do all the work. 
