UPDATED 11-10-2010!
SugarSync - This is my main service. What's great about Sugarsync is that you can have it back up your files on their server, and sync the files among multiple computers. So, my files on my home computer are synced to my laptop and my school computer. You can also access these files through any web browser, and there are apps for smart phones. You can even access them with a mobile web browser if you don't have an app. You get 2GB (UPDATED 5GB free as of 11/10/10) for free and there are fee based plans with more storage (next level is $4.99/month for 30GB). I can access my files anywhere, on any device, which makes it very convenient. You select the directories that you want to be backed up. The "Magic Briefcase" is the directory or folder you pick to be automatically backed up and synced. As soon as I save a file to that directory, it is uploaded to their servers.
The Websync feature is also nice. If you are accessing your files through the website, you can select "Edit with websync" and a Java program will download a temp copy of your file, allow you to edit and save it and then upload the new version. You can also share files with others through email or the web.
Sugarsync came in very handy for my wife. 1 week after setting it up on her computer, her hard drive died. Completely dead and no data was recoverable. If it wasn't for Sugarsync, she would have lost over 2 weeks of work (since her last backup). The automatic sync and backup is wonderful.