When you setup an IMAP email account in Outlook 2010, desktop (local) folders are automatically synchronized; with POP3, messages are automatically deleted either once they are downloaded from the mail server, or once Outlook's "Deleted Items" folder is emptied.
Click on "File" (top left) and select "Info"; go to "Account Settings > Account Settings".
Double-click on the email account to configure, and click on the "More Settings" button.
Select the "Advanced" tab.
Check the "Leave a copy of messages on the server" checkbox.
Check "Remove from server after  days" to automatically delete old emails after the configurable number of days has elapsed (between 1 day and a maximum of 100 days).
And/or check the "Remove from server when deleted from 'Deleted Items'" checkbox, and Outlook will automatically delete from the mail server emails that you have deleted, but only once you empty that folder. In the meantime, copies of these emails stay safe on the server.
Click "OK", then "Next" and "Finish" to save your settings, and "Close" to return to Outlook.
Note: repeat these steps for email account where messages should be left on the server.