Now some background for the unconvinced: The Dropbox service makes USB Flash drives, floppy disks, and emailing documents to yourself pretty much obsolete, except for instances where you can't access the internet.
Ever work on a project where emailing different versions of a document among several collaborators is painful? Google Docs provides a great solution for collaborating on simplistic spreadsheets and basic word processing files, but Dropbox is a better option for sharing the majority of folders and file types that need a full feature set like Microsoft Excel, Word, or PowerPoint. The main restriction to this approach is one you are already used to dealing with: collaborators will need to work one at a time or have to merge their changes into a new version manually.
Since launching a beta over 2 years ago, Dropbox has automated backing files up for over 4 million users using a "Dropbox" folder on their computers. Whenever a Dropbox user's computer is connected to the internet, the Dropbox folder backs up automatically to the cloud.
How could Dropbox make your life easier? Even more important than the collaborative folder sharing described earlier could be the effortless way Dropbox backs up whatever important documents you store there: perhaps schoolwork from this term, a project for work, or pictures from this year that you haven't yet backed up on DVD or an external hard drive manually--even though you keep meaning to!
Additional uses I have found for Dropbox have included picture sharing, and the mobile experience on an iPhone and iPad (and Android, I believe) allows you to read PDFs or other documents on the go. If you mark a file as a "Favorite" while you have an internet connection, you can even access it on your device when you are left without Wi-Fi or data. Lastly, I once unexpectedly needed to email a file on my computer to a friend but was nowhere near my computer. Luckily, I was able to access the file on my mobile phone via Dropbox and email an access link to that file to my friend within minutes. Space age stuff!
While there are other similar services out there like SugarSync and Box.net, I have yet to find one that allows me to do so much, so easily, for so little: free.
Still reading?!? I have slowly been researching less expensive options for larger-scale cloud storage options for when I run out of the 2GB+ that comes free with Dropbox. Input welcome!