I have multiple layers of redundancy. This is Mac-centric, but you can do something similar in other operating systems:
* I use a Time Machine to do incremental backups of my system drive which also contains any files that I don't want to lose.
* I periodically make a complete image of all my important drives. I have two copies of this. One copy stays off-site and I never have both at the same location as my originals. The other copy is local but left disconnected. I periodically rotate a copy to the off-site location. I use SuperDuper to make the images.
* I use DropBox for things I am working on and various other important files I want backed up and shared across my computers. This isn't big enough to contain the bulk of my media files (music, photos, video), but anything small enough goes here. A few of my super-important media files I keep here, like my wedding video and photos. I started using DropBox's photo syncing feature for my phone camera and am thinking of using it for all my cameras as well.
* Anything in my DropBox gets backed up by Time Machine as well on two different computers at two different locations.
I think it's really important to have at least two backups in the case that one of them fails. And one of them absolutely should be off site since a burglary, fire, hurricane, etc can potentially take them all out if they are all in the same location.
Also, it should not be possible for a remote attacker to erase all of your backups. For example, if you used a combination of Time Machine and cloud backup, an attacker could potentially gain access to your local machine, do a secure erase of all your drives including your Time Machine backup, and gain access to your online cloud backup and erase that. In a situation like that, you better hope that your cloud backup provider keeps enough backups such that you can recover erased files.
If you want to be even safer it's good to have 3 backups. One local, one off-site, and one off-site in a different city (e.g. Internet backup or shipping your drives somewhere). Now this is considering a severe worse case scenario, but having an off-site backup in the same city isn't enough, because a hurricane or earthquake could potentially damage your drives in both locations.