I havent actually tried this but i believe you do the following:
1) Click Help on any Hotmail page (usually top right-hand corner).
2) Type Close Account in the keyword search section of the Help screen.
3) Click the Close Your Account link within the Help screen.
4) Click the go to the Close Account link that is highlighted in blue.
5) Read the instructions. When you are satisfied that you understand the terms associated with an account closure, click Close Account.