I think it depends on what you mean by censoring ourselves. Do you mean filtering what we say when expressing our opinions? In that case, I feel we all the right to express our opinions without fear of reproach and condemnation. Standing up for what you believe takes courage. Condemning others for their opinions is cowardly.
I think thinking a bit before we speak or write would be a good thing; much as a Facebook thing I saw that said, "If people can be anything they want on the Internet, why do so many pick Stupid?" Hurtful things should definitely be self censored.