So, while making my knot learning table, I had thought to do a top 6 (or 8 or 10) knots in each category. Not being a practical knotter by inclination, I made my lists through 'net research. Here’s my notes in the hopes that the lists and categories can be refined for future use and/or reference by others. Most of the articles I found were disposable pop stuff, even from subject specific magazines, often having only 2-3 knots, so they would as a general rule always be the same ones.
Not including the simple/overhand/half knot or the double overhand.
general/household
reef knot - plus slipped versions for bows and shoes
surgeon’s knot
double overhand
constrictor knot
slip knot
cow hitch
? - something for tying non-gift type packages, stacks of newspapers or similar
Climbing - found a fairly good article for climbing, hence this category is more complete than the others
figure 8 - the kids have had fairly regular climbing parties. I’ve seen the figure 8 used to attach the harness to safety lines. So, a crucial climbing knot
figure 8 on a bight - similar use?
clove hitch
bowline
Prusik Knot
water knot - essentially an overhand bend tied in webbing, apparently it is used to make loops in webbing that are used for hand holds?
double fisherman’s bend - also known as the grapevine knot
alpine butterfly
italian hitch
boating
bowline
sheet bend
clove hitch
round turn and 2 half hitches
cleat hitch - attaching boat lines to the dock
sheepshank
Camping and other outdoor activities
reef knot
clove hitch
girth hitch
bowline
chain sinnet
timber hitch - name derives from actually dragging logs, also useful for bundling sticks and the like
taut line hitch
Farming - ? - many of the usual plus something for baling?
Rescue - ? - many of the usual plus some harness/makeshift seat sort of things
Fishing - this is a whole can of worms ;D that I was going to just ignore.
Craft
lark’s head - aka cow hitch aka girth hitch
square knot - aka reef knot
surgeon’s knot
slip knot - knitting, crochet
weaver’s knot - aka sheet bend aka basic netting knot
half hitch - friendship bracelets, knotless netting
Josephine knot - aka carrick bend aka double coin
simple/common whipping