The less you know about it going in, the better the experience.
This includes the knowledge that it’s good. You should forget that people praise it everywhere because that has a potential of ruining the experience. It did for me, somehow.
Undertale. I was blown away by the soundtrack and the cleverness of it all. The twist was good too, but I hated the total completion grind a bit. But it is optional.
Crypt of the Necrodancer. Again, blown away by the soundtrack and how confidently it pulled off the idea of a rogue-like rhythm game.
Insurgency: Sandstorm. This might be stretching the concept of “indie” a bit, but its predecessor was definitely an indie game. This is an excellent arcade/realistic FPS shooter.