Before commencing any upgrade, make sure you have a full backup of your existing system, including a schematic backup of your current database. In the event of something going wrong, you can always revert your database back and try again.

Custom mods may be lost when you upgrade!

View the changelog to see whats new.
Password - Important - Read First
If you are upgrading from a version older than 2.5, all account passwords will not work after the upgrade. In 2.5+ passwords are now stored using the PHP password API which uses bcrypt. This favours the less secure sha1 used in previous versions. Account visitors will need to use the 'Forgot Password' option to reset their password.

You should send out a batch email to accounts or modify your store to let them know.
How To Upgrade
For v2.0 or Later Only - Upgrade Instructions.