Tape still has a role to play in backup, and if handled properly it provides cheap and effective archiving. This video shows what happens when you don't treat it so well.
The clip was shot in the data management centre for specialist data management firm Spectrum Data. The release accompanying it explains how tape can go wrong:
Tape media in the main is made up of a mylar (plastic) substrate, covered in a binding agent that binds oxide to the substrate. The oxide then forms the data recording layer where tracks of data are written. As tapes age, the binding agent on the tapes (which is hydroscopic) absorbs moisture. The absorption of moisture has two effects. Firstly, the binding agent goes from a hardened material to soft and sticky. Secondly, it causes the tape layers to swell slightly putting massive pressure on the many layers of tape that are wound tightly against each other. The end result (known as stiction) is that the side of the tape holding the data sticks to the back of the layer of tape on top of it and in many cases results in the sticky binding agent simply peeling data off the tape layers in succession below it.
Bottom line: You won't be getting that data back if this happens. Hit the link to watch the clip.