Alternate Realities Explained
There are three main distinct types of alternate realities.
These are worlds that exist on top of our own. They may be similar, they may be completely different, but the idea is that they occupy the same space and have existed since the dawn of time. They play off the idea that anything that could possibly happen has happened in an alternate reality, all decisions that could have been made have been made, so there could even be a reality out there where Vinny didn't cast Bufu.
This idea has been used extensively in science-fiction and comic books, all the various marvel universes, the numerous Earths in DC, and the great (for the first two seasons) tv series Sliders.
These are often confused with parallel universes when in actuality they are very different. An alternate dimension is a separate "plane" of existence that exists on our world, it's just beyond our vision. These are things like subspace in science-fiction games, astral planes, or any time you enter a world where things look all funky. A lot of times this is how cloaking technology is explained, a person is "out of phase" as as such can't be seen by those in this dimension. It's also quite a popular way to depict how demons or shadows can move around without being seen. This idea is used in Deadly Premonition: the sky darkens and things appear that other characters never seem to notice.
These alternate realities are formed when time travel changes the time line of a universe resulting in a different outcome. It's like the idea of what would happen if you travelled back in time and killed Hitler. The moment you did it there would be a "point of divergence" creating a new history where Hitler never rose to power. The best example of this is seen in Back to the Future 2 where an older Biff Tannen took a book from the future in to the past and changed his own time line. This resulted in drastic changes for the world around him. This concept is used extensively in the Command and Conquer games.
This area of science is a little sketchy, some think that the point at which you alter time would create a splinter universe and yet others think the changes would be limited and localized to that universe's time stream.
These concepts have been played on throughout history in many different ways. C.S.Lewis was one of the first people to popularise the idea of parallel universes in his series the Chronicles of Narnia. There are pools that acts as portals to a great many different worlds where things are very different from our own, and the wardrobe itself could also be considered a portal to another world. Phillip Pullman in recent years used this concept in His Dark Materials, the protagonist had a knife that could literally tear the fabric of space to allow moment between worlds.
Alternate dimensions have been theorised in one form or another since the stone age. Ancient witch doctor types that take mind altering substances believed that their minds were opened to see things that existed in our world but were normally invisible to humans because they live in an alternate realm. They are also thought of quite often by various meditating types who believe in astral projection, the idea that the spirit exists on an alternate plane and can leave the body to explore this part of existence.
Alternate histories have been contemplated since man learned the ability to think independently, it's hard to look at history and not not wonder would would happen if a few things were changed. One of the earliest examples of this was written by Livy, in Av Urbe condita, in which he contemplated what would have happened if Alexander the great had expanded east and engaged in war with Rome. Another is by Louis Geoffroy in the 19th century, in which he he explored a world where Napoleon defeated the duke of Wellington and went on to rule a mighty French empire. A more modern day example is Making History by Stephen Fry, in which Hitler dies but the Nazis go on to win World War 2 without the dictator.
Really, any game can be seen as taking place in an alternate reality as it is clearly a world that is not our own. The exceptions to this are ones that take place very distinctively on other planets or in galaxies far far away such as Star Wars. In those cases, the stories could be said to exist in our universe, just somewhere we don't know about.
Some games use parallel universes or alternate timelines as one of their core concepts. Dark Void is the perfect example of a game set in a parallel universe. It exists on an alternate Earth. Another example of this in games is Spider-Man Shattered Dimensions, which is based around many different parallel Spider-Mans. The use of the word dimensions in the game's name is a popular misconception, that alternate dimensions and worlds are the same thing. Games use fictional timelines as a setting for possible games quite often, World in Conflict depicted a possible invasion of the United States and Red Alert had a very messed up timeline that I don't claim to understand.
Alternate Dimensions are used in games quite a lot. This can be any sort of phase shifting where you go through worlds, any sort of vision that lets you see things normal people can't, worlds that exist on top of our own, or creatures that exist but can't always be seen because they live beyond us.