Q: How do I log out my Apple ID from every device ?

Hello Antonate,

Here are two ways to manage the devices associated with your Apple ID. 

For iPhone, iPad, iPod Touch and Computer: Associating a device or computer to your Apple ID

"I'd like to remove unused devices or computers, associated with my Apple ID."

"I'm not sure which devices or computers are currently associated with my Apple ID."

1. Open iTunes.
2. Sign in to your Apple ID by choosing Store > Sign In from the iTunes menu.
3. Choose Store > View My Account from the iTunes menu.
4. From the Account Information screen, click Manage Devices.
5. Click the Remove button next to the device name you would like to unassociate.

http://support.apple.com/kb/ht4627

Computers Only, not iPhone, iPad, or iPod Touch

"I tried to authorize my computer, but it says I have five (5) computers authorized."

"I don't even know which computers I've authorized in the past."

"I do not have those computers anymore."

Deauthorize all computers

1. Open iTunes and click iTunes Store.
2. Click Sign In and enter your Apple ID.
3. Click your Apple ID and select Account.
4. Click Deauthorize All.
   
   The Deauthorize All button appears only if you have more than two authorized computers.

You can only do this once a year.

http://support.apple.com/kb/ht1420

Good luck and have a great day!

P.S. This question ideally belongs on the Apple Support Community > iTunes > iTunes Store community board.