I have what might be a silly question, and since the site's down, I can't find out for myself...
Could I play this as a singleplayer game? And if so, do I download it and keep it on my computer? I don't really want to pay to access servers for a game that's still in alpha with no guarantee of the servers staying up - if I pay, I want to be able to run it all on my computer, if that makes sense. Keeps my game from going poof.

There is singleplayer and multiplayer. However, you download updates and authenticate with the server.
Currently, I am able to play offline mode (which I assume is just SP), but I am kind of waiting for the patch before I continue.

Meh, I think I'll pass then. I'm fascinated by the concept but my internet's terrible here on campus, so I pretty much can't play anything that requires internet access.

Well it depends if you would enjoy it as it is currently. So far I've sunk at least 40 hours into it so already have my moneys worth for 10 euro. If you don't enjoy building though you may want to hold out until the adventure/fighting part of the game is fleshed out more.
Nah its not like that, you can download a single player client and just to patch the game you will need internet. You could quite happily use the version you downloaded without logging onto the net in singleplayer. Also its like 450kbs for the entire game(uses more as you explore but still).

Hmm...I'll have to try it then! There's a demo, aye? If it'll run on my computer, this looks like EXACTLY what I've been looking for...for a very long time!

Check minecraft.net to play Alpha for free. It looks like there are some server problems, and Notch made it free to play until it's fixed.

Hmm...I don't have an account. I did download it though. I tried just clicking 'login' and got an odd error.

Write anything in user and password boxes, and then click login. Works for me.

Nope, gives me a null fatal error (5) and tells me it couldn't extract something. And I did give it full permission, so I don't -think- it's my computer (running Windows 7 here).

Redownload it and log in. Worked for me, I had that same error just now.

Redownload. I DO have an account and had that problem, so I just grabbed a new copy of the exe.
Just a shame that the server is down for now. I want to wear my Captain America jammies, god damn it :p. Skins are supposed to work, but I am stuck as default.

This is the most epic game ever. 'Nuff said.
(oh, and I'm buying as soon as the server issues are fixed).

After buying this game yesterday, I ended up playing it for the next ~7+ hours. I'm kinda scared of starting it back up today.

I think this might be one of the most perfect games ever. Finally dragged myself away from it to go get food and finish my studying, but dang...I'll probably be up half the night playing this :D

Downloaded this "game", actually it's new form of digital crack, last Saturday to check it out on the free weekend. Then I suddenly realized that it was sunday...
Had my fix every day since and suddenly the dealer, whom had just fed me this substance, yanks it away and tells that if I want to "play" again I needed to pay. So I did what most sane people would do at this point: Realize that I was addicted and seek help.
.
.
.
.
Wrong. As I didn't have any money on my account but I had cash, I jumped on my bicycle and went to bank to deposit 10€. Then I came back home to buy my fix.
Hopefully this won't ruin my thesis badly...