The short answer is yes—signing petitions works.
Petitions put pressure on governments, corporations and others in positions of authority. They also make everyday people aware of important issues, making it more likely they will discuss them with friends, family, and neighbors.
The more people speak out—via online and real-life communities, social media and citizen journalism—the more an issue is noticed, and the less an issue can be ignored. Governments, corporations and societies are forced to listen and make changes.
Writing and signing petitions can work—and they have, many times. See Randy Paynter's article on the power of internet petitions, a formidable refutation of Snopes.com's dismissal of online "slacktivism."
The reason we have such apathy in society today is because most people believe it's too difficult to have an impact and/or they don't believe they personally can make a difference. Because online activism makes it easy to get involved, millions more people than ever before are speaking up and taking action. And that's a good thing. Ask any hardcore activist you know - their first action probably wasn't storming the White House. Usually, activists start with simple steps, get some positive feedback, and then take it to a higher level. If we want a more engaged democracy we need to make it easy for as many people as possible to feel the joy of those first simple steps. Internet petitions are effectively a "gateway drug" to more civic engagement.
Randy's article goes on to list nine success stories that clearly illustrate the potential effects of an online activism campaign. Read them here, then see additional petition case studies within this Toolkit.