Perhaps one of the most popular indy games in recent memory. I was never really interested in it but my brother runs a dedicated server and I seen it at Wal-Mart and decided to pick it up. As with Terraria, I basically made a handful of 'tutorial' worlds to get the hang of it. Now I'm on my first real world. Being written in Java was a real turn off for me, as I have developed with Java in the past and know many of its limitations. However "Notch" (creator) really pulled it off.
What really snagged me is that it moved from just a building game to something with a bit more meat. Survival mode as its called introduced a hunger system, hostile mobs and more recently, new dimensions to exploit. Since its written in Java its fairly easy to make mod packs, texture packs and graphical mods (such as Optifine). The world is about as infinite as is possible within a computer system. Its actually completely open ended and the only limit is the computer. Once you go so far out the risk of crashing and corruption increases past a certain point. It is estimated the playable surface area in a single player game is 8 times the size of the earth. Beyond that point the physics and terrain generation goes crazy because the x/y values are too great to be stored properly as variables.
ED: Apparently this is no longer true. The Farlands as it was known was removed and now you can only go up to 30 million meters before it starts generating "fake chunks" and if you step onto these fake chunks you will fall to your death. At somewhere around 12 million meters from 0,0 chunks start getting deleted so if you build a home at 0,0 and go out there, when you return it will generate new terrain and your home will be gone. Here is an image I found with size comparison:

One of thing that I was baffled about after playing Terraria, is how would you know if there is lava nearby? Well turns out you can hear it and if there is one block between you and the lava pool (from above) it drips through the block. Water also does this so you get an indication of what is nearby along with the sound.
There are lots of things to do surprisingly and I'm really enjoying myself. Tomorrow there is an update that adds a lot of new items and changes a few game mechanics. Looking forward to that as I can automate many of my farms, but I may end up simply creating a new world for it. They give access to development snapshots for users to test as well, which I think is a great feature. Unlike many games I play, Minecraft is still being actively developed and new features are being added every few months.
For me, one of the more enjoyable aspects is there are a handful of block destroying mobs in the game. In contrast to Terraria where there is endless whining to remove the single extremely rare mob that only appears in Hardmode. Perhaps the most popular of these is the 'Creeper'. I'm not sure what exactly its supposed to be but it can be a deadly creature if you are caught off guard. Just look at this image from my world.
Mostly filled in by bricks:

A pic of a Creeper:

Here is a view of the area I called home. I actually live in a cave here. This is the head of the cave that I use for experimenting and putting some things outside. Like the clay towers, I just did that for storage purposes. I used to have a diamond tower as well but harvested it for armor and tools. The wheat farm was a quick little project to test what I learned about redstone (the wiring system in Minecraft). It uses pistons to hold back some water and when you hit the lever it will let water flow over the wheat and wash it into a collection area. Then you turn off the water and replant some seeds. The tree farm I figured this out on my own. Oak trees you can actually plant right next to each other and create a wall of wood. Makes it very easy to harvest. The hostile mob system is a design by Etho (search youtube). It causes mobs to spawn in a specially created underground chamber and be carried to the surface by water. They are killed by lava and the drops come right out the front. Its good for collecting gunpowder for TNT.
Underground I was able to get grass down there and customized the area for my needs. I won't post any screens of it unless somebody wants to see. Then I would prolly do a tour video of my entire world. I have a Blaze farm in the Neither, potion brewing areas and enchantment rooms dotted all over the place. Along with many named strip mines.

Night view from a high platform:

So yea, anybody playing? If so show us your creations or your thoughts on this game.