Well Roblox meets all the criteria, apart from the fact it isn't good.
There are some fun servers on Roblox too though, for example my favorite server there has both teams of players on a galleon with player-operated cannons on them and the goal is to destroy the other team's ship. Last time I visited Roblox everything was so laggy I couldn't really play though.
Ace of spades for sure its a game a bit like minecraft although its a first person shooter and you have capture the flag. You can build bases dig etc. http://ace-spades.com/play/
It is a brilliant game.
You forgot WURM ONLINE which Notch also helped to start. This game is still in BETA just like MC. To me its better then Minecraft, but I cannot play it because I'm on a lousy laptop. But it IS a crafting game and you are Forced to have to survive. They have 2+ Free servers you can play on as well as the PVP Paid server. I used to have an account, but when I lost my last good computer, I got stuck on this laptop. So time for me to build another gaming machine so I can get back to Wurm.
Minecraft is a good filler until I can get back to a REAL crafting game with awesome graphics. Blocks suck.
Stranded is a Single Player non-blockish crafting game. I have been playing it for a couple weeks now and I am hooked. Took me a little bit to understand its unusual interface, but it did not stop me from playing it.
And as you can see here, it even includes a map editor. THIS IS A FREE GAME.
Spore. Just Spore. I bought the game and I'm more addicted than Minecraft. But, if you are a Pacific, you won't like the Civilization Stage. If you have been friendly in Tribal Stage, you will need to convert cities, and finding sad cities isn't easy.
There is actually a game that uses MC style but in space! Its called Blockade Runner, build your ship up however you like, pilot it, attack other ships & stations. Mine asteroids. It's still in development though but you can play it free as long as you dont mind the updates being 2 weeks behind the pre-ordered users. http://www.blockaderunnergame.com
I have to admit, that even though the game is ASCII graphics, it is a good game.
there is also a great game "MY ISLAND FORTRESS" it's a little like minecraft but alot smoother and better grafics i luv how it gets upgraded every saturday THIS WEEKS UPGRADE IS A BOW AND ARROW AND A FEW OTHER THINGS NOT TO SURE YET BUT THE GAME IS PROGRESSING ALONG VERY RAPIDLY IT WILL BE MOVING ONTO MULTIPLAYER SOON THERE IS ALSO A KICK ASS FORUM ON THE WEB SITE IF YOU ENJOY MINECRAFT LIKE MYSELF YOU'LL LUV THIS GAME YOU SHOULD CHECK IT OUT WWW.MYISLANDFORTRESS.COM
Not sure if you are allowed to mention them, considering the oh so much hate minecraft, but ROBLOX is a free online game where you can build and script your own games in a moderated form of LUA, where you can create games with GUI interfaces, or games using the provided characters and what not. You can actually MAKE your own crafting game, but you build everything and anything.
Roblox also provides easy connection to online interaction.