If your account was moved to the new server, I have more information and instructions (with screenshots) to set up the account in Outlook 2003 and newer at Outlook.com Migration Status.
Update July 8 2016: Migration is going a little slower than expected. People sharing calendars or using the outlook.com address to sign into their Windows phone are still waiting to be moved (and will be moved last) but others not constrained by either of those issues are still waiting. Currently, Microsoft expects to have all moved before their new announced deadline of mid-2017. You can use this link to request the move: https://mail.live.com/default.aspx?owaoptin=1.
In the next few weeks we’ll be making some updates that will impact your @outlook.com, @hotmail, @live, or @msn email account. Those changes will prevent your email from getting delivered to the Outlook desktop application you use. When you notice that you stop receiving messages, simply follow these two steps:
The message contains links to explain how to remove the Outlook Connector account and how to use auto account setup to add it back as an Exchange account. Until you remove the account and add it back, you will not be able to use Outlook to access your Outlook.com email. You'll need to log into outlook.com using a web browser.
See How to add or remove an email account for the steps needed to add or remove an account from Outlook.
The big news for anyone who uses Outlook.com for email, or to sync calendar and contacts to smartphone: Outlook.com is moving to the Office 365 infrastructure in 2015.
Many of the annoying issues affecting Outlook users who sync to Outlook 2013 and 2016 will disappear with the move: Contact Groups will work, attachments in appointments will work. See First look: Outlook.com on Office 365 for more information.
Outlook.com users will be able to use many of the features Office 365 subscribers are enjoying. This includes Clutter, which moves bulk and less important email to a separate folder. Search Suggestions and Refiners as well as Pins and Flags to quickly find the messages you need.
OWA supports link preview; after pasting a link, including links to YouTube, into your message, a rich preview is added to the message.
If MAPI service is enabled, when the account configured in Outlook color categories and flags will work as expected, as will contact groups. Mail can be imported and upload to the server, easily. Calendar sync will work.
For more information, read the announcement on the Office blog: New ways to get more done in Outlook.com