I've looked into using an online backup site a couple times. I figure I could easily find a couple free ones and backup on both to lower the chance of them losing my files. Each site normally has different specific terms and size allotted. You have to decide which one will meet your needs while being realistic. If you use 5gb one your computer you need to find/buy 5gb of backup, not try and fit it in 2gb. Here's a couple I've bookmarked as reasonably professional looking:
Free
Free Online Backup – IDrive-E – Encrypted, Secure and Automated!
Free secure online backup service - Xdrive
Cost
https://mozy.com/home (4.95/month)
BeInSync - Secure Remote Access, File Sync and Online Backup Software (55.95/year)