Flight simulators were one of the first three-dimensional PC games where the mouse could be used as a controller, to control the orientation of the camera (in other words, the airplane). The most natural mapping of the mouse axes to control the "aircraft" was, of course, to simulate the movement of the yoke (the "control stick" of an airplane), in other words, moving the mouse forwards would be equivalent to moving the yoke forwards, which would make the airplane (ie. the camera) pitch downwards, and likewise pulling the mouse backwards would be equivalent to pulling the yoke backwards, making the airplane pitch upwards.
Many PC gamers started their 3D game experience precisely with flight simulators, which is why so many people are accustomed to this "inverted" vertical mouse axis (moving the mouse forwards looks down, moving it back looks up), as it feels the most natural way. (Part of this may also be that it also simulates the movements of one's head: If you want to look down, you move your head forwards, and vice-versa.) Even many people who did not start as early as with the first flight simulators still prefer the "inverted" vertical control for the same reasons.
Fortunately the vast majority of game developers know this, which is why the vast majority of 3D games (where the mouse is used to control the orientation of the camera) offer an option to use either the "normal" or "inverted" vertical mouse axis. This is such a trivial option to offer that it costs basically nothing to implement, and it keeps a significant portion of the customers happy.
Except for a few shameful games which don't offer the option, and instead assume that everybody uses the "normal" vertical mouse axis. There is no option to use an inverted vertical axis.
For example, the game Myst III has an option to invert the vertical mouse axis for camera controls, but for some odd reason Myst IV does not, even though both games are published by Ubisoft. This makes the latter awkward to play for someone accustomed to the inverted control.
People have complained to Ubisoft about this and pleaded for a patch which adds the option. It's one of the simplest features to add to a game, and the previous game supported it, so there really is no reason to not to add it. Some people have gone even so far as to demand a refund for the game if the problem is not fixed. Ubisoft's response to this has been, basically, "we don't do refunds; we might look at this inverted vertical axis option thing, maybe."
No such patch has ever been published.
Did Ubisoft learn from this mistake when they published Myst V? Nope, that one doesn't have the option either. And people have complained and pleaded for a patch. Ubisoft is ignoring them. People can't even begin to comprehend why. They simply won't add the feature, no matter how much people complain. No reason given whatsoever.
This is especially jarring given that Ubisoft has made many, many other 3D games, most of which do have the option. It remains a mystery why they are shunning their Myst customers with this.
Of course the last two Myst games are not the only examples where, for inexplicable reasons, some game developers have decided not to include the option. You can find a list with a bit of googling. The list is not really large (a detail which in itself makes it inexplicable why some developers opt for omitting this feature even though they must know that people use and want it) but still contains too many high-quality games.
"Ok", you might say, "those developers suck, but why you don't simply use some external software to invert the mouse axis?"
Well, you would be surprised how difficult that seems to be.
There is no option in Windows, in the Microsoft mouse drivers or in the Logitech mouse drivers to invert the vertical mouse axis. Logitech in particular offers a program which can be used to bind all kinds of actions and settings to keystrokes... except for inverting the vertical mouse axis. It's just not possible.
After an extensive search I have found exactly one third-party program which can be used for this exact purpose. And this program is commercial, ie. you have to pay money for it. As far as I can see, nobody has made a free program for such a simple task, even though PC gamers have been struggling with this problem for the past 20 years.
How hard can this be, really?
(Btw, I have noticed a curious difference in attitude between those people who prefer using the "normal" mouse axis settings as opposed to those who prefer using the "inverted" vertical axis setting. While most of the "inverters" seem to perfectly well understand that some people are more accustomed to the normal setting and other people to the inverted setting, and there's nothing odd about that, quite many of the "normals" seem to have a great deal of incredulity against the "inverters". They just find it really odd that anybody would want to use an inverted mouse axis, and just can't seem to understand it. I have encountered this strange attitude both online and in real life. What is so hard to understand about this?)
And by the way, desktop computer games are not the only ones suffering from this annoying problem. There exist Xbox 360 (and probably also PlayStation 3) games where there is no option to invert the Y axis of the right thumbstick (ie. the thumbstick which controls the camera angle). This can be equally irritating as with a mouse, but even more incomprehensible. This is, after all, a joystick, and the relationship to flight simulator controls is even more glaring. Not offering the option to invert the Y axis (and only the Y axis) is incomprehensible and stupid.
Not surprisingly the Xbox 360 offers no system setting to force the reversal of the thumbstick Y axis. (There exists an option for this in the user's profile settings. However, this doesn't make the underlying system invert the Y axis. This is only a hint for games to do so automatically if they already have support for it. If the game doesn't have the support, this setting will do nothing.)
(So far I have played two marvelous counter-examples of this, where the game not only supports inverting the Y axis, but it actually determines this inversion automatically at the beginning of the game via gameplay: Halo 3 and Splinter Cell: Conviction. In both, at the beginning of the game, you are instructed by in-game characters to look up, and the orientation of the Y axis is determined automatically from that.)