You can use a Terminal command to stop this on any specific App.
http://www.maclife.com/article/howtos/how_tame_six_os_x_lion’s_early_problems
The last tip in that article has it:
"By default, OS X Lion now attempts to get you back to work sooner by opening the files you were last viewing upon launch. While it’s a nice feature for many apps, there may be cases where you don’t want prying eyes to see what you were last viewing. The System Preferences > General tab has an option for getting rid of the feature entirely (simply uncheck “Restore windows when quitting and re-opening apps”), but there’s a better way to handle it on an app-by-app basis, courtesy of developer Wil Shipley.
First you’ll need to know exactly which app you want to kill this feature on -- we’ll use Preview as an example, since it may not be desirable to have it restore documents in most cases. Fire up Terminal again and use the following command without quotes: “defaults write com.apple.Preview NSQuitAlwaysKeepsWindows -int 0”. For other applications, simply replace “Preview” with the name of the app -- when in doubt, visit your Preferences folder to confirm how the app name appears in the “com.apple.XXXX” file this is modifying."
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To see the exact way an App name appears, make sure the Finder is selected so the Finder menu appears, then up left near the Apple logo on the desktop bar click Go To, then Go To Folder, and type in ~/Library. Then in the window that opens, click on Preferences. You'll see a list of files, don't click on any. Just scroll down to the com.apple.XXXX area to see how the app you want to change appears. In this case, Safari is what one would expect, Safari with a capitol S.
So the command to type or copy and paste into Terminal is:
defaults write com.apple.Safari NSQuitAlwaysKeepsWindows -int 0
Then hit enter.
Close and restart Safari, next time you restart the computer Safari (or whatever other App(s) you ran that on) should not resume automatically from the last saved state.