Forget Minecraft, think rogue-like and buy Terraria
Terraria is a colourful and approachable sandbox game on a 2D plane, where you control a character as they explore the world, collect loot, and mine in search of new material to turn into loot, and more challenges to hit over the head with shiny new hand-made stuff. Almost all of the action happens underground, and you discover different and distinctive environments the further you go, each with different dangers and rewards. Nearly every mention of Terraria (including this one) compares it to Minecraft, but that isn't the most appropriate comparison to make. I believe Terraria is properly-speaking an off-shoot of roguelike games, going in a very different direction from the most famous descendent of that venerable line, Diablo (Terraria does, however, colour-code loot like its distant cousin does). Like in roguelikes, you have an open, procedurally-generated environment, where you measure your progress by how deep you have gotten and correspondingly how advanced your equipment (found and self-made) has become.
On the action side of things, Terraria can't compete with the complexity of most dungeon-crawlers, with their hundreds of different monsters and dozens of magical status effects. But the crafting here is much more intricate and rewarding, and that comes straight out of Minecraft. That is how Terraria sets itself aside from the pack, making use of the valuable lesson Minecraft has taught us that it is one humdinger of a motivation to play a game when you are able to meaningfully shape the world through your own work. For a small downloadable game to offer this much is quite an achievement, and I heartily recommend it to all comers.
The only criticism I can offer is, firstly, that the sound and the music becomes repetitive rather quickly, and secondly, that it suffers from the directionlessness that plagues many sandbox games. Once you're about halfway in it can become hard to stay focussed, or to know what you should be doing. This very much comes with the territory, but both these criticisms only come into play once you've spent a dozen or more hours at this $10 game, and it's a testament to Terraria how long it manages to stave off this particular worry, and how rewarding it is to keep playing. Every time thus far my interest has started to flag, I discovered something new: a floating island high in the sky, or the entrance to a dungeon eerily suggestive of what your own handiwork would end up like if, instead of you clearing the world, the world were to get rid of you. That provides a nice little sting to the tail (one straight out of Dwarf Fortress, another very creative off-shoot of roguelikes). You should try it out.