Scott Hanselman has a "definitive guide" that will help you migrate from your existing mail solutions to Google Apps (Premier Edition). He moved his entire family (wife, parents, brothers, cousins, in-laws) to Google Apps, and there wasn't a single solution for everyone. Scott had to buy a software to migrate Microsoft Outlook calendars, email and contacts, and create AIM Mail accounts to move local archives to AIM's IMAP folders that can be imported using Gmail's migration tools (a feature of the Premier Edition of Google Apps).
The guide also offers a hack that lets you transfer your email from one Gmail account to another Gmail account (it should work for normal Gmail accounts too):
The solution is two-fold. First, in the original Gmail account, make sure you've enabled POP Email in Settings|Forwarding and POP and selected Enable POP for ALL MAIL.
Then, logout, and login to your destination account in Google for Apps and from Add an Email Account, enter in the Gmail username and the POP Server as 184.108.40.206. Also, note the non-standard port 995. Don't select "Leave a copy" because Gmail won't let you anyway. However, don't worry, your emails won't be deleted in the source.
The conclusion is that Google still doesn't offer enough tools to make the migration painless and without buying/using third-party solutions.
Google, Google Apps, Guide, Knowledgebase, Gmail