Also, the question is: do you trust Facebook when it tells you that no information was shared? How would you know if it was?
To remove the unauthorized applications, go to your Facebook Account details (top right corner), select the Application Settings option from the drop-down menu and delete unwanted applications by clicking on the "X" mark. I would also recommend editing the settings for those applications you want to keep using - browse through them and see what you want to share with whom and what do you permit the application to do.
These latest privacy changes have wreaked havoc on Facebook, so this is the right time to consider which information could be too sensitive to be provided in your account.