Don't use Google then if it worries you that much. If it's sensitive data then putting it on the web or usenet is your own fault. Don't use Picasa, their desktop search utility or IE toolbar and you won't have any possible chance of leaking data to Google. I'd trust my stuff with Google a lot more than Microsoft and plenty of people do that already. The MSN portal, Hotmail and Terraserver all do the stuff you're scared of.

Google doesn't index the entire web. It falls short of that by a significant percentage from all estimates. Nobody does it all.