Helping people with computers... one answer at a time.
Windows Live Hotmail changed the approach you use to change your password. I'll provided step-by-step password changing instructions for Windows Live.
I can't figure out how to change my password since they changed MSN Hotmail to that new Windows Live Hotmail. How do I change my password now?
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This remains an extremely common question.
Let's walk through, step by step.
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First login to your Windows Live Hotmail account, and then click the Options link in the upper right:

And then at the bottom of the resulting list, click on More options...:

On the resulting page, click on View and edit your personal information:
At this point you may be prompted to re-enter your password. This is a security measure to prevent just anyone from walking up to your computer and changing your information.
There's something interesting to note about the screen that you land on:

Note that it stopped talking about Hotmail. This is your Windows Live account.
Why does that matter?
Because your Windows Live account is used for all Windows Live services including Hotmail, Messenger Spaces and more. When you change your password for Windows Live Hotmail, you're also changing it for all your Windows Live based services.
Near the center of that page you'll see a section labeled Password reset information:

Click on Change on the Password: line and you'll get this box:

Naturally you must type in your old password in order to prove that you are who you say you are and are authorized to make changes.
As you type your new password the new Password Strength indicator will show you just how strong your password is. Having a strong password that's difficult to guess is incredibly important to the security of your account. Make sure you always have a strong password.
As an additional security measure you can instruct Windows Live to automatically require you to change your password every so often. While this can be seen as annoying, it's actually another layer of security to protect your account from theft.
Click on Save and you're done.
Article C3168 - October 4, 2007
my email account has apparently been hacked into and i want to change my password.
Posted by: bonniebartley at November 19, 2011 5:40 PMBrilliant! Sorted my wife's hotmail problem, many thanks
Posted by: Rev. Nic Deane at January 11, 2012 6:33 AMyes now i get how to change my password cheers
Posted by: nadeem at January 13, 2012 11:55 AMdoesn't work any longer. more options does not
Posted by: caroline at January 30, 2012 8:09 AMbring up view and personal information. where is this box now???
@Caroline
Posted by: connie at January 30, 2012 9:47 AMTry going to Options > More Options, and then reading the list there under "Managing Your Account." You'll find everything you need to change your password there.