In my opinion there are six key times you should perform a backup of your wordpress blog.
1. When You Update WordPress
The WordPress code is updated regularly, but before you even consider FTPing the latest shiny version up to your host, backup the existing code base and database.
2. When You Install a Plugin
I am guilty of plugin addiction and I install loads of new and glittery plugins to my blogs all of hte time, and I often do not backup before I do this. YOU SHOULD backup befire installing plugins. Some of them amend your wordpress database, some drastically chaneg how your blog works. Have a checkpoint to return to if the plugin causes problems.
3. When You Install/Change Your Theme
Changing your theme may not seem like a huge event, but consider that many people customise their themes, take a backup of your changes before you change themes and delete your hard design work.
4.When You Have Written Some Quality Content
The last post you clicked publish on was awesome and went straight to the front page of Digg. You need to protect this asset by backing up your content.
5.When You Install Other Applications
Many blogs have systems other than WordPress installed on their websites. I am thinking of things like forums and affiliate systems. Many of these will share the MYSQL database that WordPress uses. Backup your WP config and data before begining the install process.
This is n0t really a point in time, but my last key timing for backups is to backup regularly. Check out the many backup plugins such as Filosofo’s excellent utility and create a scheduled job to backup your blog. I have my plugin create the backup and send it via email to me. Then I simply skip the email to my archive. I know I have a daily backup ready for any eventuiality.
As a parting note backup often and soon. Keep a number of checkpoints so you can recover to a point in time.