I suppose any discussion about cloud computing should first start with a definition of cloud computing. Think of cloud computing as a a bunch of servers residing in one or more data centers accessible via The Internet. It's called a cloud because it expands and contracts on demand. Cloud computing reduces and contains IT budgets because little capital investment is required. Furthermore, IT management is greatly reduced so that your in house IT folks can focus on more strategic issues. System maintenance and upgrades are mostly performed without notice.
Company financial data such as accounting applications or applications that store healthcare information may not be such a good idea on a public cloud. But using the power of the cloud for applications such as process tracking, shipping, and even inventory management is being highly adopted by both commercial businesses and the federal government. Security standards for process tracking, purchase order processing and receiving non purchase order shipments are usually far lower than those mentioned above since no personal data is captured. In fact the federal government entity NIST typically rates applications such as a low security risk.
If security still concerns you have your vendor describe the security controls implemented for data in transit and at rest. A good vendor should be able to show you how data is secured in both instances. Simply providing secure data transport over SSL isn't enough.