What's the Islamic Ruling in participating in public protests? More specifically like the protests happening in the middle-east today.

The Assembly of Muslim Jurists (AMJA) fatwa committee have issued a statement in regard to the participation in such demonstrations.  Its conclusion is that it can be different from one country to another while the default of peaceful civil protest is that it is permissible.  Each situation should be judged by itself  as by its scholars and leaders based on the benefits and harms.  As for what we have seen in Egypt and other Muslim countries, I believe that it was correct and may Allah make the outcome of such change in the Muslim world positive and good for them and their future.