I upgraded almost eight blogs powered by WordPress yesterday when I got the release news of WordPress 3.3.1.
WordPress 3.3.1 is now available. This maintenance release fixes 15 issues with WordPress 3.3, as well as a fix for a cross-site scripting vulnerability that affected version 3.3. Thanks to Joshua H., Hoang T., Stefan Zimmerman, Chris K., and the Go Daddy security team for responsibly disclosing the bug to our security team.
The good part is that update procedures are pretty simple.
visit Dashboard → Updates in your site admin.
Actually, I update themes and plugins first. Then update WordPress.