Thee are certainly plenty of them out there. But what would you consider the most useful, and therefore the ones you need to know cold, that you can tie behind your back, eyes closed, with rain pouring from the skies... Maximum of three, not counting variations.

I would nominate the figure eight, the clove hitch, and the trucker's hitch as three that are highly useful in a variety of circumstances. A few years ago, my number one choice would have been the bowline and its numerous variations. Over the last few years, the climbing community has been moving away from the bowline toward the figure eight because of its demonstrable greater security.

Obviously, the more knots in your reliable repertoire, the better, and there are always knots that are perfect in some specialized applications, but that are not always best in more general usage (like the bow knots we tie every day when we lace up our shoes).

My choices come from a technical climbing and caving background,along with some nautical experience, and that obviously influences my choices. What are your favs, and why?

The three knots you named are good. A knot rarely mentioned but very useful is the Prusik.

Overhand knot (and permutations._
On a bight, it is quick, can be done one handed, lays flat used in webbing, and is stronger than a figure eight knot (harder to untie after loading tho)
Tie twice (correctly) and have a square knot
Use in the tail of a rope to backup a bowline
To connect two ropes for abseil (Euro Death Knot)

Joining two ropes together:
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The Zeppelin Bend

End loop:
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The Anglers Loop

Adjustable loop:
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The Tautline Hitch. This is certainly not the best sliding loop available, but you said I had to be able to tie it behind my back, with my eyes closed, in the rain!

There's a whole lot of other useful knots, but you limited it to three! Didn't even get into the hitches or stopper knots - maybe you should expand your rules to "five or six knots".

square, surgeon's, bowline

Definitely! There are many, many useful knots, just the thing for specialized and unusual applications. I like a bowline on a bight with asymmetrical loops for multi-point anchors or hoisting 1000 pound mammoth skulls out of a pit (real case!). But this is not something i do every day.

I am thinking of knots one knows cold, and can tie in very demanding conditions, when speed is of the essence, and one can't tolerate mistakes or booboos.....

If one has three versatile knots down cold, then definitely expand the repertoire. The sky is the limit, once one has a good foundation.

Good point. You can often substitute knots as well. Say, you have forgotten how to tie that hitch you used to love so much to attach your rope to a tree. Nothing wrong with throwing a bowline around that tree (with a safety overhand or two on the tail end). Not necessarily what a bowline was designed for, but a useful substitution none the less. I'd much rather put a bowline to use like this than to try (and fail !) to remember that fancy hitch I used to know, get it wrong, and fall to my death over a cliff because of an improperly tied knot letting loose.

I did the whole "knot" thing when I got serious about mountain climbing. A long time ago, but I still remember my knots.

I only use about 3-4 of them. It's enough to do everything - pretty much.

Loop In A Rope - Climbers don't use a normal knot, but instead the Figure-8 knot. Easier to untie, after the rope has been stressed.

Webbing - standard knot is the Water Knot. Everyone who works with webbing probably knows this one.

Joining 2 ropes - my most important knot. The Double Fishermans knot. My life depended on this knot so many times, I have lost count. It never failed me.

Clipping to a Carabiner - yes you can use the clove hitch, and it works well.

Have fun.
It's "knot necessary" to know a lot of knots. Just a few that do the job.

Pte

That's a loaded question. My go to knots tend to be the following:

Loop in the end of a rope: Bowline with Yosemite finish
Loop in the middle of the rope: Alpine butterfly loop
End to end bend: Sheet bend or Ashley bend
Slip and grip: Tautline/rolling hitch
Hard tensioning: Truckers hitch with directional figure 8
Slipknot: Double overhand slipknot
Binding knot: Constrictor or versatackle
Stopper knot: Figure 8 or oystermans