The Google Buzz episode is an example of the risk of putting any data anywhere, regardless of how non-evil and trustworthy the data collector may be. I'm not saying you should pull all your data and buy a tarp and a shovel. But consider a few things.
Google didn't set out to be evil or clumsy in this case. They created the product with the best of intentions: to improve your connections with your network, and as a result make that network (that they host) more valuable to them. I'm sure "win-win" was probably said in more than one conference room.
But they made a number of mistakes, in implementation and in rollout. Most of the mistakes were minor, but amplified by "the millions that have signed up with Buzz!" A few mistakes were serious and possibly dangerous to a smaller number of people. Personal and child security were mentioned by more than one commenter.
One of the lessons learned from this, and any other misuse of data, is that your data will almost certainly be misused, on purpose or by accident. The more data, especially in one place, the more certain. I think the freelancers who suddenly had their clients exposed to each other were somewhere between surprised and horrified.
My own actions include not using my gmail account anymore, since a couple years. I use some of their products, but I don't sign in unless I need to be signed in to do something.
That doesn't mean that Google doesn't still know a lot about me. Even if I never had a gmail account they would still know a large part of my network, because a large number of my correspondents use gmail. Depending on my correspondents, I might become interesting to the Chinese government in another breakin, or I might get unwanted attention from law enforcement because I correspond with on of their suspects, creating even more potential for mistakes and misuse. The larger my actual or accidental Google network, the more likely something like that might happen.
There's nothing wrong with using Google. There's nothing wrong with using free services. But you should certainly think about how things can go wrong, and proceed from there. If you need your data to be online, it might make sense to keep some of your data with a paid for service (they aren't expensive) whose only interest in your data is the fee for keeping it secure and available; at least there's less temptation to play with it in creative ways and risky ways.