How do I encypt Time Machine with Mac OS X Lion?
It took me a little while to find the "Encrypt backup disk" checkbox, so I thought an answer explaining that may save you some time.
Press the "Select Disk…" button in the Time Machine System Preferences panel, and the "Encrypt backup disk" checkbox is enabled when you select a disk.
I decided not to encrypt my Drobo after reading Alrescha's important note about not being able to use an encrypted disk with older versions of OS X than Lion.
But I was curious to see if Apple would warn me:
(See also "If I encrypt a Time Machine backup disk, is the entire disk encrypted or just the Backups.backupdb directory?".)
Time Machine does have a checkbox to encrypt the backup, but it will read, encrypt, and write every block of the disk - which can take a long time. If you are using a new drive it is much faster to encrypt it with Disk Utility first.
The encryption is handled by the OS – not Time Machine. Lion will prompt for the password whenever the disk is attached. Once the password has been entered it looks like any other disk to Time Machine.
n.b. you will not be able to use an encrypted disk with older versions of OS X.
Time Machine backups can be encrypted as well. When setting up Time Machine, it'll ask if you want to use encryption and to enter a password.
I've not tried to restore to a new system, but I would think it would just ask for the password and work fine after you enter it.