Flower
You play as a gust of wind and you fly through a meadow/grassy field, picking up flower petals along the way. Picking up petals gives more vibrancy and color to the meadow. It's got really soothing chime music and sound effects that are a great way to unwind.
flOw
This is thatgamecompany's predecessor to Flower. You play as this amoeba-type creature that eats other amoeba and dives to deeper depths to continue eating. The art is very minimalist and nice, the sounds are calming, and there's no real objective so to speak so you can play at your leisure.
Pokémon Snap!
This one's a childhood favorite of mine. There's some effort to it, but really all you're doing is taking pictures of Pokémon. There are a lot of cool secrets to, and you can replay levels all you want so there's never a rush to find everything in one go.
Portal
I could see how this game might frustrate some people, but the plot is so minimal that I feel like you can take this game as slowly as you want. I think everyone can enjoy puzzle games; it's just that some might need to enjoy them slower. I like to take my time with the puzzles, and I never get flustered because I don't feel any sense of urgency to finish them as soon as possible.
Artoon
This game was originally available on Xbox LIVE Indie Games service but has been removed for whatever reasons. I'm never deleting it off my hard drive because of that. It's got a really great art style and a lovely soundtrack that varies between stages. You basically bounce around and try to touch each platform in the level before jumping on the finish line platform. You can do the basic job of hitting every platform, or you can use special bounces and avoid touching a platform twice in order to rack up maximum points. It can be occasionally difficult, but again, no one's rushing you and you don't have to do it perfectly.