When going to the set up pages for all the Social Plugins, they now provide example code using an APP ID.
http://developers.facebook.com/docs/plugins/
Is an APP ID now required for the Like Button and other plugins? What happens if an APP ID is not included when using the plugins?
I've checked the Facebook developer blog and read about the Like Button Migration. I haven't been able to find a straight answer for this either there or in the FB Like Reference.
Notice:
This is an old dated information, the official facebook's behaviors are changed.
Simply, the answer is No, just look at the following official Facebook resource.
Notice: To do it without need to the app id, you have to visit the above page when you are signed out from Facebook. Look at the following screen shot.