Online backup has its place, but it's not a universal solution. First, if you have a LOT of data, you can get into bandwidth concerns. I've heard that Carbonite throttles your uploads if you try to upload "too much" data.
Be sure to TEST your online backups periodically. A fellow consultant using a "business-leve" online backup service found that, even though the online backups were failing, he'd receive no notification at all.
If you are going to need a large amount of data INSTANTLY, you won't get it from an online service. The pricier ones will airship you a hard drive with your data in an emergency.
Unless you do your own encryption, it's certainly possible that an online service could read your data. You'll have to decide if you trust them.
The ultimate backup is one that's offline and offsite and secure. Online backup meets those general characteristics pretty well. The only thing missing is that you really should have "full" system backups, too. I've seen people lose important data because they didn't know where some of their data really is and it gets skipped in a "data-only" backup, and because re-installing an OS and all the applications is very time-consuming. An "ideal" backup would be at least a monthly local FULL SYSTEM backup image, combined with ongoing "important data" backups that can be on the Internet if you wish.