Zingtea said:
Vampire: The Masquerade - Bloodlines is set in present-day L.A, but it's still about vampires and magic and stuff. Good game, but perhaps not what you meant, OP.
I was going to mention that. It's essentially our world, but it's an alternate universe known as the World of Darkness. In that respect, it's about going around and doing your magical things without humans finding out - which, as a character points out, is difficult when almost everyone has some sort of camera phone with them at all times.
Another is The Longest Journey series. It's set in our world (but further in the future), the world of technology, that sits in parallel to a world of magic known as Starc. The characters can switch between each world, and face whatever is going on with both as the boundaries between the two slowly collapse.
Basically, our own world is boring on its own. But a world filled with technology to combat and study nature cannot mix with magic which essentially does the same - it's like having two different means that gain the same effects. It can't work that way. And we're getting bored of technology, and want to turn to magic. So, we need to create alternate worlds to see how this works - usually set in a period of time completely devoid of technology, since we can't imagine a world that has progressed without it. It's a horribly post-modern and Western idea, but it's the dominant one.