Security is often a priority for these companies, and therefore you should rest at ease when you are investing in one of these services, as your data security is often the number one priority. If you are concerned, speak to cloud storage providers about the measures they take to protect your documents and information from being accessed by others.
In regards to worrying about whether or not you will lose data by accident, many cloud storage services have an inbuilt disaster recovery facility, allowing people to recover their important data even if the system or software has a fault. Again, this is a top priority for these service providers, and certainly not something that users of such a service should ever be too concerned about.