I am the admin for a number of organizations that I set up for specific, not very long term, projects. I don't want to see some of these organizations any more, but I don't want to lose their data. Can they be archived?
SteB's answer is right, but I think you'll find it helpful to know that after you delete the organization you can still view the boards by clicking the
Boards menu on the top right by your profile pic and then click
View Closed Boards at the bottom of the menu. You'll find your all your boards are available even though you deleted the organization they were associated with.
When you re-open the board it will show up in your My Boards list.