The hottest cloud computing application right now is Dropbox. Dropbox stores your selected files “in the cloud,” or (more accurately) on its servers. More than that, Dropbox can be used to sync files across computers. It comes with 2 GB of free storage and there are upgrades available. It’s a pretty useful tool.
I use it with 1Password to sync my password database across devices and to back up some important files. Lifehacker has published a number of articles including how to Use Dropbox for More Than Just File Syncing and How to Use Dropbox as a Killer Collaborative Work Tool.
(Oh, and if you use my referral link, you and I will both get an additional 250 MB of storage free)