In reply to Andy Hardy:
This advice is particularly useful. You don't want/need a huge number of knots in climbing. More than about 10 is probably getting dangerous as you'll only mess them up. I think in my regular climbing I know and use only 9 as far as I can remember (if that). Libby Peter's book has more knots than you'll probably ever need and has a whole load more useful information about how and when to use them in addition!
The ones I use are below:
1) Figure of 8 (on a bight and re-threaded) - Used every time I tie in
2) Clove hitch - Use it repeatedly/extensively to build my belay anchors
3) Munter/Italian - Had to use it recently when I forgot my belay plate at the bottom of a pitch (to the immense chagrin of my 2nd!)
4) Overhand - Would use it in EDK style if I ever had to connect two ropes for abseiling. Can't remember the last time I used it if I'm honest, but I'd say it's a must-have (if only as a stopper knot on the end of a rope)
5) Double Fisherman's - creating loops out of cord
6) Water knot - creating loops out of tape
7) Lark's foot/girth hitch - slinging spikes/threads/anything where I don't trust it not to ride up (also the first step of a prusik knot)
8) Prusik (would use a pair when ascending a rope)
9) French prusik (for abseil backup/rescue, as it can be released under tension and is super easy to tie)
Because I only use a limited number, I know them intimately, I can tie them blindfolded if necessary, I know how they work and how they'll respond, I trust them wholeheartedly, other people know them and can inspect them, etc. KISS is a hugely important rule of climbing.