Having a reliable automated back-up system in place is crucial. While backing up to a physical, external hard drive is helpful, those can fail as well, and if there was a fire and your hard drive and computer are together - everything could be lost. Because of this, online backup is recommended, when possible.
Should you need back-up for work with a department within the University, email email@example.com.
These providers might offer a free period, but you should be aware there will be a paid option at some point.
HMS currently offers CrashPlan for faculty and staff (but not students, unless you're working in a campus-based department). You can subscribe to your own backup service from CrashPlan through their site, http://www.code42.com/crashplan/.
You CAN test drive it for 15 days for free, but this will require your credit card information.