I seem to remember some concern that on-line petitions are not considered a legimate measure. I've seen people discouraging others from participating in on-line petition protests because they're not "real".
It basically depends on 1) who you're petitioning (your city? Congress? etc.) and 2) what identifying information you collect on the petitioners. So, if you're petitioning the city council to start a recycling program, having an online petition with a bunch of people from out of state (or even out of city but in your state) means little to nothing to them. Governing bodies want to see petitioners that are their constituents. If you're petitioning the federal government in some way, you can accept petitioners from any state, but overseas petitioners do you no good. Similarly, your petition must have some mechanism for indicating 1) the legal name and 2) the location of residence of the petitioner. If you've got a petition filled with Wilma Flintstones, that doesn't help. Nor does a bunch of Orlando residents signing your petition to the city government in Boston. Basically, the mechanism (online vs. paper) matters very little, but the content (and verifiability of the content) matter quite a bit.
Good luck, whatever you're petitioning!
crafty mama to Chloe and Emma (10/08) and Piper emergency medicine PA and single mother by choice