I love some of the ones that PPs listed - the t-mobile, the do-re-mi and the opera one.
There is a flash mob that is very special to me - not because it's so amazing but because the women in the video were protesting gender segregation in their city. the segregation issue in that city came to a head when one of the young girls who were the target of extremists agressive and violent (both verbal and physical) attacks, spoke up. backed by her family, she stood up and spoke out against what was going on and this video was done soon after the story hit the news: http://www.youtube.com/watch?v=pZd0kLWP01c
I don't know that family personally, but i used to live in the city and i know many of the people in the video.