My dirty dozen-ish: tautline hitch, bowline, square knot, figure eight + variants, fisherman's knot, N half hitches, sheet bend, Zeppelin bend, trucker hitch, Alpine butterfly, hangman knot, and a variant on the shoe knot that doesn't come loose. Can't remember the name but in sure you can find many variants with a search.

Square knot most people already know. Tautline and bowline are the two worth memorizing being able to do soaking wet in the dark.

Personally I rate the figure-8 over the bowline. I think it's a much more versatile family (and much easier to tie and inspect with high confidence soaking wet in the dark).

Good point! I think I mentally chucked it with the square knot under "knots that should already be in most people's inventory" but you are right, that is definitely worth learning, since there are so many useful variants.

So like, 4 essential knots: Figure 8, square knot, bowline, hitch. The map, filter, fold, and reduce of knots, if you will. Most everything else can be composed from those.

Not the parent comment, but you'll get a long way with a figure-8 (both on a working end and on a bight), a clove hitch, and an alpine butterfly. I'm sure others have a couple more favorites.

(this is omitting a few "foundation" knots like the overhand)

Learn a munter hitch, it's extremely versatile and can do everything from securing something, to belaying or rappeling off it (with a locking carabiner). It is an extremely important knot for setting up rescue systems as it can hold a load under tension, yet can be undone and slack added to the system while under complete control.