All,
I posted this over on BW for all of you that are dying to join your school's Facebook group and learn about your future classmates, but at the same time don't want your coworkers or boss to find out you are leaving. This set of instructions walks you through removing the groups list from your profile page. Enjoy!!
After you log in, from the home page there should be a grey block on the right side of the screen that says "Applications". At the top of the box you have things listed like Photos, Groups, Pirates, etc. Click on the top right button that says 'Edit'.
It should take you to a screen that says Application Settings - Recently Used. If Groups isn't listed then change the drop down to 'Bookmarked' or something else until you see 'Groups' listed. Click 'Edit Settings' and then select the 'Profile' tab. Where it says 'Info Section', choose 'Remove'. Then click Okay. Check your Profile page and it should be gone.