Yume Nikki is an indie game by a guy called Kikiyama.
Take a look at the Wikipedia article.

What makes the game interesting, is the fact that not much information is given to the player. Therefore, there is an intriguing sense of mystery, i think there is a small back story, i believe it covers the tragic events that occoured to the character some time ago, these events are said to have influenced the content of her dreams. I'm not sure though.
There is so much left unexplained that there are lots of theories players have thought of to fill in the gaps.
http://www.theneitherworld.com/yumenikki/index.htm has a bit more info.

Now this is becoming a review.

So yeah, check it out if you like, it's certainly very surreal, and at times somewhat a bit un-nerving.
It's freeware, and you can get it here

I just watched some videos for this. What a ♥♥♥♥.