When you store data in a 3rd parties cloud you have to assume that the Cloud provider (Microsoft, Amazon, RackSpace, etc) will keep your data secure. If you need to be sure that your data is secure, then a Cloud platform may not be the correct choice.
It really depends on the application. I was at a cloud computing user group meeting recently and asked around about this same question.
For some uses, attendees suggested, you can just encrypt everything, and use it as a storage-as-a-service. In other cases, more and more vendors are letting customers deep dive into facilities and to see exactly how the data is being secured. It's never absolute, but then again, security never is. Just have to determine the acceptable risk and work from there. The Microsoft, Amazon, RackSpace's of the world likely won't give you this "inner" peak, but often smaller vendors will.
Federated Identity Management, Proper Encryption techniques with Key Management for Data, Network Security measures, Virtualization Security and Physical Security are main areas while considering Cloud Computing.