Remember that list of BNP members that found its way onto the web a while back? Some of the those names and addresses were apparently people who'd simply put their name to a petition.
I don't sign them out of principle, if I feel strongly about an issue I don't really want my name added to a list of people who were too polite to say no, and have likely not given much thought to the issue at hand. My main beef with petitions though is that the number of signatures collected has no context. You could present a petition with a 1,000 signatures, but how many people did you solicit for those signatures? 1,001? - that would be evidence of a pretty strong public will. By what if you'd asked 2 million people to sign and almost all of them refused? Those 1000 signatures don't really mean much then.
Anyway we all know the real way to effect change in a modern democracy is to start a facebook group call "I bet I can find a million people who want / don't want {insert something glib or inevitable}" and then refer to this as a 'campaign'.