I don't know if there is a standard, but I like that mine point out to the side and turn to the middle to go on, even though they turn in opposite directions. I can get them both on with an elbow without the spout getting in the way. I also think it looks better that way, but I'm sure that's a personal preference.

Either way you like them to point, most cartridge faucet knobs can be independently reversed (inverted) to please you.

On the bathroom sink round handles both turn counter clockwise to open. Lever handles both pull towards the front to open.

"On the bathroom sink round handles both turn counter clockwise to open. "

Only if you have cheap Chinese faucets.

Classically the hot and cold have turned in opposite directions.

"I'm a right-tight, left-loose kind of guy so it always made me crazy to turn the cold handle the "wrong" way. "

Having the handles turn in opposite directions has been used for a long time, and is even better with levers instead of knobs.

"I have a widespread faucet with cross handles. The were installed by a previous owner to turn as if they were levers. I'm a right-tight, left-loose kind of guy so it always made me crazy to turn the cold handle the "wrong" way. "

I had this problem as well - it arose because the faucets could be ordered with lever or cross handles, but the valves were the same either way (and not reversible). I had to order an additional one of the cold valve (or hot, forget which) to get them to turn correctly.

These were Grohe, so not cheap (although perhaps Chinese now).