On the Hotmail page, click on Help > Enter "close account" (w/out the
quotes) in the Search box > ...
<QP>
How to Close a Hotmail Account
To close a Hotmail account, stop using it. After thirty days any unused
account becomes inactive. After ninety days, the Passport becomes inactive.
You can also close your Hotmail account from within the account itself. To
do this, follow these steps:
1. Click Help on any Hotmail page.
2. Type Close Account in the keyword search section of the Help screen.
3. Click the Close Your Hotmail Account tip within the Help screen.
4. Click 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.
NOTE: After an account has been closed, any folders and e-mail associated
with the account are deleted and cannot be recovered.
</QP>
Source:
http://support.microsoft.com/kb/316659