There are services that synchronize a local folder to the cloud, like dropbox you mentioned, and Windows Live Mesh (it has a new name now - I don't remember it), and probably more.
The advantage of these services is that all files are also stored locally, thus improving response time, supplying a local copy in case of failure in the service (I believe those services are reliable, but having a local copy adds another level of protection)
Online solutions on the other hand don't use you local storage (although this is often not a real issue, and are alway up to date (file synchronization may take some time, so you wont have always the most recent copy.
one service that provides this functionality (including a free version) is http://www.swissdisk.com/