Alternate Worlds? Options

I'm curious to know what the people here think of when in terms of "alternate worlds." As an example of what I mean, in a number of books and shows, the main character is summoned by one way or another into a completely new realm. One that tends to be heavily based on fantasy and magic. A simple example would be "The never-ending story."

Do you guys think completely alternate realms like these exists? Places where magic is closer to a basis of life than just a taboo hobby.. Personally, I think it would be really cool to have such places, but I highly doubt anything of the sort really does exists. (Of course there is no real way of answering both until someone here whips up a teleportation spell of some sort! Ha.)

I'm not sure if 'fantasy' worlds exist as in those created within fictional books but I do know that the Native Americans used to believe in three worlds. The one we have now, the afterlife and the in-between. They used to put on masks so the spirits could take over and they could act within the in-between world.

That's what I read. I hope it's right.