First, let me start by clearly pointing out that no matter how much data you have, you always should have a backup. No matter what that backup is, online or offline.
What is an offline backup? An offline backup is any kind of backup where your data is stored on removable media such as a memory stick, CD-ROM disk, DVD disk, or external hard drive. Years ago, the primary storage device for offline backups were tapes. Tapes are no longer a viable solution for a lot of backups because they lack the storage capacity and are more expensive per gigabyte than other forms of storage.
What is an online backup? For purposes of this post, we'll define an online backup as being a backup to a 3rd party internet backup service such as Carbonite (www.carbonite.com) or Mozy (www.mozy.com).
So what is the difference between online and offline backups?
Online backups: Your backup can be retrieved from any computer in the world that has access to the internet. Most online backup services backup your data in the background so you never have to think about running your backup or keeping it up to date. Plus you are protected if your offline backup is lost, stolen, or destroyed (fire/flood/malfunction/etc).
Offline Backups: You can backup to an offline media faster than it takes to upload all of your data to the Internet. Same goes for recovering your data - faster recovery time.
The most secure approach to backing up your data is to use a mix of online and offline backups. So your backup has a backup (so to speak).
For offline backups: I recommend the Maxtor OneTouch External USB hard drive. It includes everything you need and is very easy to setup and use. Once you have the drive setup, you simply press the button on the drive itself to backup your system. They range in price from $75 to $350 depending on how much storage you need and you can purchase them at many office supply and computer stores.
For an online backup solution: I recommend that you give Carbonite a try. I've used both Mozy and Carbonite and they both have comparable features. One thing I did like about Carbonite over Mozy was how easy to setup it was - the install program TALKS you through the setup. Mozy had more options about what to backup, but for a novice, options can be confusing. One thing I did like about Mozy was that they will send you a DVD copy of your backup (for a fee) if you don't want to wait to download all of your files in the event of a system restore, Carbonite does not offer that at this time. Carbonite was also less expensive per year for a single computer and offers unlimited storage. Time spent recovering data from an online service should be a critical factor if you are looking at online backup solutions for your business.
For the conspiracy theorists' out there: I have not looked into the companies that own Mozy or Carbonite so I cannot confirm that they are worth trusting with your data. As a technology professional, I would tell you that it is highly unlikely that anyone at these companies would want to sort through the millions of user accounts, petabytes (that's 1,000 terabytes, or 1 million gigabytes) of data to look at YOUR stuff. But keep in mind that your data (no matter how encrypted) is being stored on someone else's system. If that bothers you - than online backups are not for you. I would suggest that you purchase two (or more) of the Maxtor OneTouch drives I've recommended above and store one (or more) in a bank safe deposit box, and keep one at home.
Other helpful reading: PCMag.com review of online backup providers