Leaving
If you feel that the principles of the organization you are in do not match up with your own principles, or you just want to leave based on other reasons, you can use the Leave Organization feature. It can be found on the Organization Preferences screen, however please note that this feature is not available to organziation leaders. You are an organization leader for a reason!
Actually leaving the organization is as simple as clicking on the Leave Organization link on the Preferences screen, and confirming that you really want to leave the organization. A notification will be sent to the organization leader, and you will be rendered orgless.
Please note that even though you have left the organization, people can still find out about your organization affilations, previous and current. This is especially true for affiliations with official organizations, as they are what the game is all about. Whenever you apply to become a member of an organization, the people reading your application will see the last official organziation you have been member of.