Some things to think about while you contemplate the idea:
GOALS: It is critically important to have clear aims for any petition. Who are you petitioning? Exactly what do you want them to do? Do they have the legal power/authority to do it? Are they apt to respond to an Internet petition? Have they ever responded to a similar petition like yours before? Have you tried other methods to solve the problem about which you are petitioning?
NUMBERS NEEDED? How many petitioners do you think you can get to sign your petition? Beyond your family and friends are there a large number of people who understand the issues you are raising and who will back you because they share the views you express in the petition? How many signers will you need to have any significance? For an in-state project, it might take several thousand signers before anyone takes notice. For a national project you will need hundreds and hundreds of thousands. You are aiming to make a grass roots statement of political power. Can you get the numbers to "speak" power? How? Large organizations and governments don't respond to midgets.
DEFAULT POSITION: If the petition falls flat- with little to no response or action- what is your fallback plan? Shouldn't you have other ideas in mind, or do you just drop it?
RISK MANAGEMENT: What are the risks for you and others who might sign an Internet petition? Have you run the petition idea by your lawyer and/or others with experience? Is it well-written and clear; does it avoid name calling or slander? Have you considered whether the petition will make matters better or worse? What if it fails to get the desired response? Will it improve or damage your image, your credibility, your thinking, your ideas, your original aim? Are there legal ramifications that can come back to bite you and those who sign the petition? If the petition fails in its expressed aims will there be backlash? Will it infuriate others in the system you are petitioning - and cause them to close their ranks?
DISTRACTION: Is the petition a waste of time in the sense of being a time-consuming distraction from actual things you might do with less risk and greater potential payoff? Are you avoiding the hard emotional work that might have greater benefit?
Getting 25 or 50 of your friends to sign your petition is probably useless. They are signing it just for that reason - being your friend or family member. On the other hand if you talk with 25 or 50 strangers of which some end up signing is in the end more beneficial to your cause. You have created an awareness of your issue which you can then build upon. To put it another way - a person in power can ignore hundreds or even thousands of signatures. It becomes harder though to ignore 25, 30 or more who are screaming at their door - writing letters and becoming involved in your cause.
REMEMBER: The American Revolutionary players tried unsuccessfully to petition King George. The fallback position was the Committees of Correspondence and then the Revolutionary War.