How about the game Limbo. Its on Steam for around 10 bucks I think. Very well made puzzle/adventure game. Im pretty sure it meets your requirements.
IDK about that. There's no blood, but only because it's all in shadow. The ways you die are actually very violent and graphic.
Sorry, Xen, as that is a great game, but Rod is correct in that it is, indeed, very violent. I remember coming up on the spider (boss?) and getting impaled by one of its legs and then being tossed away in two pieces. -- From Psychonauts - Lungfish Civilian: (describing Goggalor) He's impervious to bullets! ... and love! --
But... a hard request, as they're aren't a lot that don't fall into these categories.
As was mentioned, Nintendo has a lot of games along these lines that are very entertaining, but stay away from the violence, gore or even realism...you might have better luck there.
The recommendation for Portal / Portal 2 is a good one, as well. -- I am only one, but I am one. I cannot do everything, but I can do something. And I will not let what I cannot do interfere with what I can do.- Edward Everett Hale