Here's a quick look into Minecraft.
It's a Sandbox game that allows you to build whatever you want basically. You try to create a shelter for yourself for when at night, monsters come out. You punch trees to get wood. You make this wood into a workbench. You use your leftover wood to make a pickaxe to mine coal, and sticks. Look for some coal, and make it into torches to keep monsters from spawning near and in your house. If you want, you can change the difficulty of the game to peaceful, to make any monsters already spawned, disappear. Now the rest of the game is yours.
If you need help, there's a Help section on the site, that provides videos on how to create a house, survive your first night, and so on.
The cool thing is not just this aspect. You also have Multiplayer. You can connect to other people's Minecraft servers and build or survive with other players like yourself.
You can also get mods for Minecraft, which change how the game looks, or adds new gameplay aspects altogether. Such as new mobs, more items to build, new tools to work with, and etc.
This game will give you hours upon hours upon hours of great playtime, whether it's solo, or with others.
There's a great community to talk with if you need help, or just talk with in general.
Did I also mention you can change how your character looks? If you select profile on the minecraft page, you can choose some skins you can download at the Skindex to change your appearance. You can look like a ninja, Micheal Jackson, a Creeper in disguise, and much.. MUCH more.