Minecraft - a very 'blocky' (in a good sense) sandbox game developed by Markus 'Notch' Persson. There are two versions - Minecraft Beta and Minecraft Classic.
Minecraft Beta is much like Stranded II, you obtain resources by destroying blocks, but unlike in Stranded, in Minecraft you can literally destroy everything in the each time randomly generated world. The world generates itself further as you travel across it.
There are so many things to see - secret dungeons and deep caves, high mountains and lava pits. Lately, Beta has so-called 'biomes', so in the randomly generated world there are different 'zones' with different landscapes - like forests, deserts, tundras (snowy forests) etc. Minecraft Beta has Singleplayer and Multiplayer modes, although multiplayer is very new, so there isn't an official server list - you can connect to other servers knowing their IP address. The only pity about Minecraft Beta is that it costs 14.95 euros (25% off during beta).
Minecraft Classic is a free browser game (although there are community-made clients) where you get different blocks at start and you can build anything you can imagine (and anything that fits the map size). There are lots of multiplayer servers you can join with different mods that make the game even funnier! I have a server in Classic myself.
Links:
Official game site
Game wiki
Game forum
World of Minecraft fan-site (they made the WoM Minecraft client)
Other links:
German Minecraft forum
Russian Minecraft site