-- the bowline, for putting a slip-free loop around something
-- two half hitches, for putting a cinching loop around something
-- the clove hitch, for tying a rope to a pole or other cylindrical object
Start with those three, tied properly, and you can do a lot.
I would add a couple of other useful hitches: the taut-line and trucker's. Along with the bowline, I use these constantly for attaching adjustable-length lines to things and securing items to vehicles.
They are both a part of my repertoire also. The trucker's offers a great "quick and dirty" mechanical advantage for tying things down on your car, on your boat (my mast when I trailer it, for instance); heck I even use it to tie down my trash-can lids to keep the animals from getting into the trash (raccoons, not bears!).
I'd 2nd the bowline - very useful knot. I was once forced to learn to tie a bowline behind my back - seemed fairly useless at the time, but then a few months ago I had to tie something onto the back of the wetsuit that I was wearing - to my amazement I did it first time - muscle memory is an amazing thing.
Eskimo bowline is non-exploding, nevertheless I wouldn't use bowline (or eskimo bowline) while rock climbing without somehow securing the working end.
Kalmyk loop (which is exploding variant of eskimo bowline) is probably not secure enough for rock climbing, but better than bowline for other tasks. Less likely to spill and easier to untie.
In climbing, a great property to have is to be able to identify if a knot is tied correctly by just glancing at it. Figure-8 is obvious. A double bowline is fairly easy. Not so sure about other knots...
-- the bowline, for putting a slip-free loop around something -- two half hitches, for putting a cinching loop around something -- the clove hitch, for tying a rope to a pole or other cylindrical object
Start with those three, tied properly, and you can do a lot.