Being able to backup as much data as you want is a BIG reason to get online backup. As your personal data or company grows you will want larger size storage.
If you use server racks (in a company), having an unlimited online storage will cut your expenses on new rack systems. Save cash and get more.
Your company can save 90% on new storage server racks simply by delegating the task to an online storage facility instead. You will save labor and the cost of purchasing equipment, IT time and more. You will not need to keep repurchasing new equipment to replace the older fault prone units.
When magnetic storage tape is used, it is always limited. See here for a .pdf overview of problems with magnetic backup tape. If you have ever tried to get data off of a tape backup, you know it is TEDIOUS! To get one small piece of data may take hours, days or weeks. You must go through the whole tape each time. An online remote backup file is quicker and easier to find data fast.