There are at least two issues: one is the confidentiality of your data. You have to examine the contract to see who owns the data (are you transferring rights to them to any degree), to see if they maintain any data that you delete, and to see how much responsibility they will accept for security breaches. If your data is important, it should be handled by a contract rather than an "agreement" and they should not reserve the right to unilaterally change the terms.
The second issue is actually how the user managers their own data. If your data is on your computer and it's important, you need to back it up. If your data is "in the cloud" and it's important, you still need to back it up. Keeping a copy on the provider's servers and on your hard drive is usually sufficient, though you have to be aware of the limitations (especially if it is a synchronization service rather than a backup service).