Shattered Pixel Dungeon - This is a variant of the original Pixel Dungeon. This version is better balanced and has more content. Available for PC, tablets and phones. Source: over 2 years ago

Pixel Dungeon and it's many of it's modded versions are free of grinding and financial transactions. Some modded versions have grindy typical RPG aspects added to them, but most don't. Most if not all mods should be available if you are open to using an android emulator. Pixel Dungeon classic is unforgiving and will do it's best to kill you. Shattered Pixel Dungeon is a much more expansive mod of the original that... Source: almost 3 years ago

Terraria - This classic title has been around for a very long time. It's a game about exploration, base building, and adventuring in a sand box world filled with bosses. I haven't played much of Terraria, but if I remembered correctly, there are various classes you can choose to build your character into, such as a summoner, wizard, melee/dps, etc.. Another game with a similar element of play, but focusing more... Source: over 1 year ago

There's also something like Terraria and Starbound if you enjoy going on adventures with a bit of a RPG element as well as building. Source: over 1 year ago

Starbound has one of the best soundtracks of any video game I've played. Source: over 1 year ago

Starbound: Includes a race called The Glitch, a medieval society of robots created by persons unknown in an experiment to understand how societies form. I'm not actually sure if the post-beta builds did anything with that lore, but nevertheless you can play as one and find settlements of them out in space. Source: almost 2 years ago

Terraria and Starbound (also great titles to play) is a pixel RPG adventure with build elements. Most of it is focused on the adventure/RPG with the building being a minor element to the game. Source: about 2 years ago