Security is probably the main concern when it comes to tapes. We've seen a lot of companies move away from tape specifically for that reason.
But for companies that have very large investments or requirements for these tapes, security becomes a great concern, particularly when looking at compliance. Take PCI for example, where you are handling private or personal information that can not end up in the wrong hands.
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Tape encryption is especially needed in this instance if the tape media leaves your premises, which technically, if you're following backup best practices, it should. You should be sending a copy of your backups to a vault site, so therefore you want that added level of protection and should the tape become lost, it won't end up in the wrong hands. Encryption makes the data unreadable without the encryption key.
Check out the entire Tape Encryption FAQ.