strange behavior: applications closing on window exit

Normal OS X behavior is to keep an application open even when the last window is closed, yet when I close, for instance, my last window in Safari, the process quits. Any changes I made to the toolbar are lost, as if it is not quitting smoothly either, like it is crashing.

Also, other programs do the same - Google Notifier quits is I close the preferences window, as if clicking the preferences close box is the main program's close box.

Is this some preferences problem? Permissions? Anyone experiencing similar behavior?