Has this really not been responded to? Depends a little on what you really
need to back up, and how you are syncing now. If you are using Outlook, all
your contacts, calendar entries etc are safe there. After upgrade you just
sync the 'new' phone and those are restored, so-to-speak. There is the free
Microsoft MyPhone web option that will capture a great majority of the files
on your phone and you can send them to the 'new' phone. For files that are
on a memory card, they are safe, though I would remove that SD/Mini/Micro
card when upgrading. Files on your phone itself can be accessed and copied
to a folder on you PC using file explorer if you are running Vista or Win7
or ActiveSync if you are running XP.  After upgrade, copy them back.

Now, applications and settings. While there are third party backup programs,
like SPB Backup, I wouldn't recommend trying to backup a 6.1 device and
restore to a 6.5 device. It would be like backing up a Vista PC, doing a
clean install of Win7 and trying to restore. If it would even do it, there
are structure and capability changes that don't transfer cleanly and would
leave you with obvious and insidious issues. Don't even know if the current
Windows Mobile programs would let you do it. They used to, and it typically
caused more trouble than it was worth. You just re-install your apps. Even
the ones you loaded onto the SD card. While the apps will remain, the
registry entries on the main device need to be restored.

You are probably aware a Windows Mobile update flashes the new image onto
the device, removing everything that used to be there. It's not like an XP
service pack, or even an upgrade install of Win7 over Vista, where things
can be retained. One reason that upgrades may not be offered that often is
the hassle of applying them and the tech support that it would generate for
the run-of-the-mill user.