Here is my list of favorites. I chose these knots for their versatility rather than knowing 200 knots that are perfect for only specific purposes.
1) Bowline on a Coil
2) Double Figure Eight
3) Clove Hitch with Quick Release
4) Water Knot
5) Munter Hitch
6) Swiss Seat
7) Hasty Rappel
8) Kleimheist
9) Tautline hitch
10) Double Sheet Bend

I believe any one or a combination of these will fill every emergency need.