If you're getting this error when running backups via Central Admin in SharePoint 2010 then the most likely cause is that the SQL Server, where your Site Collections are, does not have access to the folder you are backing up to. Meaning, your Farm configuration is on multiple machines. Mine is on 2 machines. A Web Front End (where I run the backups from) and a SQL Server machine.

You probably configured the back-up to write to a lettered drive on the Web Front End. Don't worry, I did this too then I realized that it would be best to make a Shared Folder that has the correct permission so thet BOTH machines have access to write to the same location. Then it worked.