It depends on the political system of your country, and the governmental processes that determine whether or not an idea becomes, eventually, a law. Petitions are an excellent way of gathering public opinion and support for the introduction of a new law or reform of those deemed out of date.
In the UK a new form of petition was introduced online - e-petition - which basically allows for that petition to be read out and debated in parliament if a threshold number of 100,000 names is reached. So in theory if I wanted to bring in a new law against people who wear ten gallon hats on Sundays I could get an initial airing in the House of Commons because 100,000 other people agreed with me!
That would be a start. The law itself might not never get beyond this first stage but at least the petition would have helped raise the issue. I think they are worth it because they reflect people's opinions, build momentum for a cause or change, and give politicians something serious to think about in between massaging their egos and photo opportunities.