This one is perfect for Minecraft fans.
Majic Jungle Software brought us this awesome The Blockheads and you can get it for free, both for iPhone and iPad.
The idea is the same as Minecraft: you get a random generated world, with all kinds of resources (stone, wood, iron, water, fruits, animals, etc), mountains, lakes, caves and weather, and is up to you to explore it, build on it, and do whatever you feel like.
The game is user-friendly, with simple one-touch commands to move and perform actions. This game also reminds us of Terraria, so one would say it’s a blend between Minecraft and Terraria.
If you’re into exploration of worlds, this is a must have, since it’s free and Universal.
You can also invite friends to visit your world, and communicate via voice with excellent quality.
Try it and let me know how it goes!