This is a game I just recently found out about and even though its actually still in its ALPHA stage I would still say that this has got to be THE funnest sandbox construction game I've ever played and I just felt like i had to share it with you guys. (note, there is a classic version you can play for free, but its pretty crap compared to the alpha version of the game. The game costs about $13.50 but buying it now will also leet you download all future updates, new content, and new versions of the game for FREE)
My attempt at a summary: Minecraft is by its very definition a sandbox game. Every new game you start randomly generates a world that I think is actually supposed to be about 1/3 of the size of our actual planet earth. When you first watch a video on youtube or something of that nature your first expression may very well be "Omg the graphics are so retro, old school, and pixelated" and it's true, they are, BUT if you can overlook the graphics this is a truely awesome game and has a TON of replayability. What you do is plain and simple, establish a shelter, expand, explore, and survive. "Survive?" you ask? Well in the game world day and night last about 10 minutes each (10 may be WAY off for all I know, but thats what it feels like as I play fullscreen and dont keep track of time) and during the night, several types of baddies spawn (skeletons, which shoot arrows, zombies which are your typical zombies, giant spiders, and big green things called "creepers" that explode if you get within one block of them, most likely killing you and creating a giant crater) and they spawn ANYWHERE where it is dark (I'll go into this further in my tips for starting out section). I could honestly go on and on about this game but that would take up a whole post.
My tips for starting out in minecraft: Ok, I'll change this. I WAS going to type it all out but its hard to describe unless you actually see it so I will just recommend you to this video http://www.youtube.com/watch?v=ylVtj-1Ccgg