Why does Safari restart when quit?

Question

Any time I quit Safari, it starts up again. If I quit it a second time, it will stay dead and won't restart itself. This includes when I am trying to restart my Mac; Safari and everything else quits, but then Safari immediately re-opens and cancels the restart (or shut down). I have to quit Safari a second time and then initiate the restart again.
Why is this happening? Why might it happen with ANY app? I'm afraid it's due to something I did/installed to keep Safari alive, but I can't figure out what that might be or how to make this stop.
I'm currently using Safari 5.1.4, but this has been happening for a while (years I think, but I'm not sure).

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins and log in as Guest. For instructions, launch the System Preferences application, select Help from the menu bar, and enter “Set up a guest account” (without the quotes) in the search box.
While logged in as Guest, you won’t have access to any of your personal files or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. Same problem(s)?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
Note: If you’ve activated “Find My Mac” or FileVault in Mac OS X 10.7 or later, then you can’t enable the Guest account. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards. Boot in safe mode and log in to the account with the problem. The instructions provided by Apple are as follows:
Be sure your Mac is shut down.
Press the power button.
Immediately after you hear the startup tone, hold the Shift key. The Shift key should be held as soon as possible after the startup tone, but not before the tone.
Release the Shift key when you see the gray Apple icon and the progress indicator (looks like a spinning gear).
Safe mode is much slower to boot and run than normal, and some things won’t work at all, including wireless networking on certain Macs.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem(s)?
After testing, reboot as usual (i.e., not in safe mode.) Post the results of steps 1 and 2.