Undertale! Even though I haven’t actually played this, I watched a Let’s Play of it (courtesy of Steam Train, have a look!) and got really into it. I love the different ending possibilities and the characters were amazing. I really wish I had played it myself rather than watch it though because now I know what happens and if I play it myself the effect will be spoiled. I don’t want to say a lot about it in case I ruin any plot but trust me, it’s really, really good.
Honourable mentions: Gone Home, Silent Hill 2, Bioshock