Everyone.  Ok, maybe not everyone, but most people.  Most companies experience some data loss, whether accidental file deletions or lost laptops.  Some companies experience major data loss, maybe a database server crashes, or an email server dies.  Ideally, they have a backup solution in place.  Ideally it works.  Ideally, they have tested it and are confident in it.  For many companies, it isn’t a top priority, and the testing happens when they really need it, after some disaster or data loss.  Even tech-heavy companies lose data or have gaps in their backup strategy.  I have personally had sleepless nights trying to recover data that was backed up but untested (if you trick me into a few beers, i may even tell you about nearly losing a company’s ERP database).  Some people a lot smarter than anyone writing or reading this have had data loss impact their jobs and lives.  What is lame is that it could all be avoided by backing up properly.  Here are some examples:
Ma.gnolia, the online bookmark competitor to delicious lost data in January ‘09.
Journalspace shut down in January ‘09 after a PO-ed ex-employee zapped their database, which wasn’t backed up.
The Linkup online storage company lost 45% of user data on 8/08/08

These are companies that specialize in tech-heavy data management, and they didn’t have themselves covered.  Do you?   Here comes the commercial…if you don’t, ask your IT consultant about The Backup Plan, or do what you know you need to and start backing up!

To answer this question, let’s ask another question: What are you backing up?  And another: Where are you backing it up?

If you are backing your stuff up remotely, yes, absolutely, definitely.  It should be encrypted as it leaves your machine, in transport, and on the service provider’s server.  Luckily, this is almost always the case.  Service providers do this to cover themselves.  they do not want visibility into the content you are backing up.  They do not want to be associated with the loss of your data should there be a security breach on their end.  A common method is that the user/customer defines an encryption key (like a password) that is used to scramble all data as it is backed up.  The data can only be unscrambled by using the key.  The customer defines that key, so only they can unscramble their backups.
If you are backing up locally, it depends on your requirements.  If your location is secure, and everyone with access to the backups is trusted, then maybe you do not need it encrypted.

What are you backing up? First off, there is some data which should always be encrypted.  To meet HIPAA or SOX requirements, patient and financial data should be encypted in any state (that is in the original storage location as well as in the backup).  Social security numbers, credit card numbers, anything raising privacy concerns, blackmail materials, etc. should always be encrypted.  On a personal computer, keep in mind that you might have tax records, bank account info, and possibly healthcare info saved on your machine.  If so, you probably want to encrypt it.  If the content of your computer is limited to iTunes music and pictures of your dog in the sweater your aunt knitted, you may not need encryption.  For everyone else, it would be valuable to check to see if your current backup method allows for encryption.

Oh, and don’t forget your encryption key.