In Brazil, a new law can be proposed by regular people if it gets one million signatures. While congress doesn't have to vote these proposals (they can basically postpone voting them forever), some of these have indeed become law.

The most recent one was proposed in 2009 and became law in 2010, changing the requirements to run for office (making them somewhat tougher on corruption).

PS: That law was nicknamed "Ficha Limpa". Something like "Clean Slate".