In my experience, it's a pretty near universal standard for things that can be rotated to tighten or loosen them to get tighter when turned clockwise and looser when turned counter-clockwise. (The title of my question is from a mnemonic for the directions that's commonly cited in my dialect.) This is true of things that have a fixed direction (such as screws and sink taps), but also of things like twist-ties that can be fixed either way. (The only common exception of which I'm aware are things like taps for dangerous substances, where the manufacturer wants to prevent them from being released by someone turning the tap without having to think about what they're doing.)
Is this standard as common as it seems? Are there any regions where most or even many things tighten and loosen in the opposite directions?
In regions where this standard is dominant, how did it become so? What was it like before standardization?
I can tell you that the direction for turning wood screws to tighten them was formalized in England in the late 18th century, which was when wood screws were first mass-produced.
Prior to this, wood screws were handmade and were not standardised in direction or in size. Using a screw shape dates back thousands of years to wine presses (crafted from wood) which, being individually made and not having to conform to a larger system, were not standardised in direction.
Source: One Good Turn: A Natural History of the Screwdriver and the Screw -- Witold Rybczynski (2000).
The only common exception of which I'm aware are things like taps for dangerous substances
To expand on this from the mechanical aspect:
A number of rotating mechanical applications where the torque applied would tend to loosen the fitting also use reverse threading. The instance I'm familiar with is pedals on a bicycle where the right side pedal has a left hand thread since the turning action would tend to loosen a right hand thread.
http://www.parktool.com/blog/repair-help/pedal-installation-and-removal
Other applications can be found in various engine fittings such as crankshafts and belt pulleys.
Righty tighty lefty loosey makes sense from a biological standpoint.
If you look from the perspective of the right arm, turning the forearm clockwise(supination) is a stronger action than turning the forearm anticlockwise due to the muscles associated with supination(biceps brachii,supinator) are stronger than those associated with pronation(pronator teres).
As a result because most people are right handed it makes sense you want the stronger action to be the one you use to drive the screw into the object.