Is there an easy way to move from a Hotmail account to something else, like a Gmail account or a new Hotmail account?
Without losing all the folders, emails, contacts, etc.
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You can use Windows Live Mail to download all your Hotmail messages, and then copy them over to your Gmail account. (Instructions here) You don't need Outlook.
Note that you'll have to have IMAP enabled on Gmail in order to use this method.
Transfer your contacts
Transfer your messages
Simply follow the following steps:
Courtesy of Wikihow.
GMail has recently updated the import settings when pulling from another account to include contacts and mail messages. The steps provided by Google GMail Help are found here: http://mail.google.com/support/bin/answer.py?hl=en&answer=117173
This may not be as complete a solution as scoopdreams provides but is an option for basic migration.