First, I would like to say that I install locks for a living. While I do a lot of locksmith work, I do not call myself a locksmith, because I strictly work on locks for buildings. That is, I don't crack safes or open cars. I own a company that specializes in selling and installing residential and commercial door hardware.
I just stumbled upon this question, because with all of my expertise, I was actually wondering the same thing. I know the thread is pretty old, but I feel like I can contribute for posterity. So, here's my take:
There are basically two types of locks on doors: cylinder and mortise. Mortise locks are comprised of a rectangular box that fits inside of a, well... a mortise, which a carpenter cuts into a door. Because of their design, the key is inserted into one side, and the latch attaches to the other. They cannot be reversed, and they can only be installed one way. There are four types: left hand, right hand, left hand reverse bevel, and right hand reverse bevel.
To understand the types, it is easiest to first understand cylinder locks. While mortise locks are still manufactured and used, they have fallen out of favor over the years. This is mostly because they require a skilled carpenter, or a specialized machine (which no one makes anymore), to install. A cylinder lock, which is what you probably have on your home, can easily be installed with a drill and the proper bits. They essentially just fit into a hole.
Cylinder locks can be reversed, because they fit into a round hole instead of a rectangular mortise. So, unless you have a curved lever or latch, they are all the same. The only time they are "handed" is if they have an exposed piece, which is meant to be displayed in a certain way. Even then, they only come in left and right hand. The "bevel" refers to the angle cut on the striker, so that the door closes without you having to turn the knob first. Even if a cylinder lock is handed, you can still rotate the bevel to face the door frame and strike plate when it closes. Thus, there's no reverse bevel.
If you're still with me, there are four types of mortise locks, because the key can only be inserted into one side, and the bevel of the striker cannot be rotated. There are four types of doors. The hinges can be on the left or right, and the door can open into or out of a room.
With mortise locks, the key was always inserted vertically, and the key was turned towards the frame to lock and away from the frame to unlock. Likewise, the thumb latch on the inside operated the same way. So, it makes sense that a cylinder lock should be installed the same way, since locks have worked this way for at least a century.
However, there are some nuances to cylinder locks, which prevent this from being a universal rule. The actual locking mechanism of a cylinder lock has a flat piece of metal that connects the inside and outside of the lock and passes through the latch/bolt, which holds the door closed. This is called the "tailpiece."
If the correct key is inserted into the lock, you can turn the tailpiece left or right, 90 degrees, from the outside. The tailpiece can be freely turned by the latch without a key. If you held just the locking mechanism, you would see that the tailpiece has a total of 180 of free rotation. THAT is why this question exists in the first place. You can install almost any cylinder lock in the unlocked position with the thumb latch in the vertical OR horizontal position.
So, here's what I do know for certain. Some manufactures design their locks to function one way or the other. From what I understand, this is because there is more tension on the lock when it is turned until it stops. If you think about it, and remember that the tailpiece turns 180 degrees, there is tension on the pins of the lock when it is turned left or right, but none when it is in the middle (the vertical position).
I know that this is confusing, but some locks are designed to be under tension in either the locked or unlocked position. It deepens on the manufacturer and model. I will say that, when the direction does matter, it is always noted in the instructions. So, check those first and follow them.
Also, to obfuscate things more, some manufacturers make locks where the latch sits at a 45 degree angle. All cylinder locks only have to turn 90 degrees to function. So, these particular locks tilt towards the frame when locked and away when unlocked. But, they never rest in a vertical or horizontal position. Schlage makes many models in this style.
Lastly, I have also seen cylinder locks with labels on the faceplates. Some have an arrow or mark for the locked position. Others actually have the words locked and unlocked etched into the plate. To further complicate things, I have seen these labeled faceplates with the locked position vertical, horizontal, and in between.
TLDR: All locks are different. Follow the manufacturer's instructions. If the direction is not specified, then install the lock so that it is unlocked when the thumb latch is vertical and locked when it is horizontal. The latch or key locks when turned towards the frame (strike plate) and unlocks when turned away. Whether that is clockwise or counterclockwise depends on whether it is a left or right handed door.