Possibly this question depends on location. I'm most interested in the US convention.
I have read here a convincing claim about sink faucet handles: when there are separate hot and cold handles, cross handles (knobs) should always turn on counter-clockwise, but lever handles which are off pointing outward should turn on by pulling them toward you: that's counter-clockwise on for the left, hot handle, but clockwise on for the right, cold handle.
What about a double lever handle for a shower, where the two handles, which are wall-mounted, are pointing outward and might turn either up or down?
Here, you are generally standing looking down at the handles. Is down on, which would be counter-clockwise for the left/hot handle and clockwise for the right/cold handle, matching the sink configuration? Or is up on, which has the same feeling of "pull toward you" but is actually opposite in terms of the direction of rotation?
Up (which typically stops at 90 degrees horizontal) is on. Down (vertical) is off.
"on" should be handle-up. That is for ADA reasons. A motion-impaired person needs to be able to turn off the hot in a big hurry with a motion that will, by circumstance, be both frantic and awkward.
However, that shouldn't exist.
The reason is the whole legionella fiasco and water heater temperatures. You have to keep water heater temperatures below 115F to prevent scalding, but you have to keep water heater temperatures above 140F to prevent legionella bacteria from using it as a breeding ground. This creates a safety deadlock that can only br resolved by either anti-scald faucets (which must by nature be single handle), or on-demand water heating which doesn't store hot water.
Obviously some people choose to simply ignore one safety factor or the other, and legionella is an easy target since our understanding of the threat is quite new. Grandpa goes "in my day, nobody ever got legionalla" (they didn't get HIV either, or to be more precise, legionella was there all along but we lacked the diagnostic ability to identify it, so it was misdiagnosed).
In one of our bathrooms the tub/shower has the old Price-Pfister double valve with levers. When off the valve levers are oriented down; to open they are both swung outward: to open it's CCW for the cold and CW for the hot.
The other bathroom has a shower with "old style" Price-Pfister two valves with cross handles handles (not levers). These valves work in the same sense as those in the shower/tub: cold is CCW to open and hot is CW to open.
(The lavatory faucet in the same bathroom has a Price-Pfister double handle with levers, but they work opposite to the shower. To open it's CW for the cold and CCW for the hot.)