Yes, as it is proof that you bought the game. You don't if you pirated the game...but don't pirate the game as it is illegal and Mojang is awesome!
You must register your account to play Minecraft, however, anyone can download Minecraft.
You need a premium Minecraft account to play online with other people.
Go to Minecraft.net, log in using an account that had bought Minecraft and then click play in your browser under the Download Now! button on the main page. If you do not have an account that has paid for Minecraft then you can play Minecraft Classic for free.
No you don't have to be premium on Minecraft to play it you can play the free Classic version.
A premium account can play full Minecraft through a web browser.
Stealing someone's account is not allowed by Minecraft. You can buy the game and get your own account to play.
It is free to make an account on the Minecraft website, but you have to pay to play the game.
You need an account, yes. When you start the minecraft program, it needs to log you in to your account.
You need an account to play minecraft multiplayer.
If you have a cracked client, sure.
No but you can play Minecraft Classic
Minecraft is all about the account you made, you can log into that account on any computer, you are not forced to play it only on the computer that you purchased it on.