The easiest game I've ever played is probably Higurashi: When They Cry, which is stretching the definition of 'game'; it's a visual novel with no options. All you have to do is click or press a button to make the next line of text show up on the screen, and save when you want to take a break. (Unless you consider the game to be 'solving the mystery', in which case it isn't easy at all.)

If you let me know the consoles you have access to, any genres or themes you're interested in and any subject matter you'd particularly like to avoid, I can try to come up with some easy games that might appeal!