SOPA is the only one I can think of and then they rebranded it

Petition only work if there is actual political power behind them.

There is at least one country that allows petitions to force a referendum on any law. Switzerland.

Naturally such a system develops to a consensus democracy. The reason beeing that a group that is big enough can force a referendum on any law that is passed. So the laws that are passed are usually some sort of consensus.

I would love to see some data on this. A lot of times people tell me that one way to solve social issues to get start some type of activism (march to the capital, start a rally in your town, etc). However, I haven't seen much data on the effectiveness of those things.

I had the same thought a few weeks ago (specifically about Change.org petitions). Here is a page I found that shows petitions that achieved some action: https://www.change.org/victories

No idea on how many did not succeed.