It depends. A colleague of mine had success with a petition for his local county. The county was trying to deny gay veterans the right to march on Veteran’s Day. They successfully won via petition, but were prepared to go to court in the event that the petition was unsuccessful.
I think the mass scale petitions are less successfully. They can be useful if they have a very, very high target number, but the petition on its own (say for a federal issue) probably won’t impact much change. Still, I think that, if nothing else, online petitions are a successful grassroots information sharing system. Without online petitions many people would be uninformed that certain issues exist at all. The petition can at least alert them to look into the issue and decide whether they want to do anything about it.
Regardless of whether or not I think it would be successful, I still sign the petitions for issues that I care about and pass it forward to others who might be interested.