As with the previous article on Exchange 2010 to 2013, a migration from Exchange 2007 to 2013 will also see multiple changes. That list is on the same page as the Exchange 2010 list.
First, connecting to SharePoint via OWA is no longer supported:
At one time this was touted as a great integration feature of being able to access these documents from OWA. This was actually discontinued in Exchange 2010, but it bears repeating here.
Next, ISINTEG is no longer used. This tool was great for working through your mailbox database issues while the database was offline:
The new way to repair databases is a PowerShell command new-MailboxRepairRequest. This command will enable you to see if there is any corruption in a mailbox or mailbox database, even do this as a report only (what if) scenario if need be. The tool logs events in the Event viewer as well. Link to the 2010 version is here.
Last,but not least is the Managed Folders is no longer in Exchange 2013.
Retention policies and tags are now used to help you cope with your users Outlook folders.
Hope this list provides a quick view of what has been discontinues from Exchange 2007 to Exchange 2013.