SugarSync offers limited, free online backup
Of course, 2GB probably isn't enough space to backup all the important files on your computer. But the free level makes it easy for you to try the service before deciding whether to shell out some cash for a paid account. And if do only want to back up a handful of documents, nobody will pressure you to pony up any cash.
If you're just looking for an online backup solution, there are certainly other services including Carbonite and Mozy that are cheaper. But as we discovered when we checked out the service last year, SugarSync offers a few services you won't find elsewhere, like the ability to backup files from your mobile phone and access your files from anywhere.