If you enjoy Minecraft you might want to check out Voxatron. It's a voxel based constructible/destructible environments. If you grew up playing Robotron you’ll likely enjoy Voxatron.
Another two games that feature a sandbox - constructible/destructible - environment are Terraria and StarBound. Unfortunately, even though it is still available via Steam, Terraria is no longer consistently updated and StarBound hasn’t been "officially" released yet.
I used to recommend Ace of Spades and Cube World. Ace of Spaces was bought out by a game house and Cube World development seems stagnant at the moment.