Which data service are you refering to? Are you using a broadband data package or are you just getting data charges on your phone?
If its the latter, then you're probably accessing Mobile Web or VCast. This can happen accidently a lot of times too due to the initial shortcut keys. Every plan comes with access to mobile web, vcast, etc, but if you DO access them you will be charged 1.99 per MB used (rounded UP to the nearest MB). To prevent this from happening, sign up for My Verizon and add block features to everything you are not covered for on your plan and you should no longer see the data charges appearing on your bill. If you have MB usage for THIS billing cycle, then you can add the VPAK feature and backdate to make sure you're covered (only do this if your MB overage is greater than the cost of the VPAK feature).
Yes, please elaborate on the type of data plan you are talking about.
PDA's will be charger per kilo used if you were able to get the data plan removed. This doesn't seem to be an option with newer PDA's.
But like risu said, if you are talking abou the vcast data package, accidentally hitting mobile web can bring in usuage if you do not have premium network blocked. Less than a few seconds in mobile web normally doesn't register (glad for that), but downloading game, music, and apps will from the Get it Now.