Judging by the recommendations above, I'd add:
Kentucky Route Zero
Superbrothers: Sword & Sworcery
All take a beautiful approach to storytelling, have wonderful art and sound, and are strange, unique experiences. Obviously games can do all sorts of things (I also enjoy stuff like Rocket League & first person shooters) but those five are by far the most involving, emotional games I've played and the ones I respect most as pieces of art.