Dropbox just saved me weeks of pain, so here it goes.
If the Dropbox introduction video doesn't convince you, here is my real world use of Dropbox.
I'm a University student that lives away from home. I decided to bring my desktop to my new residence. I also bought a new laptop so I could work outside of my residence.
Here's the problem, all my files are out of sync. I can work on one of my essays after class in one of the many labs across campus. But once I get home, either I can only work on the essay on my laptop, or get a USB drive, move it to my desktop and work a bit. And if I want to work outside in one of the labs again? Save it to the USB, transfer it to my laptop and get going.
While this is possible, it's just a massive waste of time if you compare it to better solutions. This is where Dropbox comes in. If instead of putting that file on my USB, I save it to my Dropbox folder, I can reach it wherever I have an Internet connection because it will sync to my computer.
If I take the time to set up the desktop Dropbox application, I can do even better. Create a folder structure inside the Dropbox folder that's automatically set up, and it will sync all my changes immediately online, and to any places I have Dropbox online.
If I open my laptop and my desktop at the same time, I can sync my files across computers immediately, in real time. That saves a lot of time.
If you've ever forgotten work at home before, you'll kick yourself for not using Dropbox.
I save all my work on my Dropbox folder. Due to a special promotion, it has over 20GB of storage currently. What this means is that anywhere I have an active Internet connection, I can retrieve any of my work.
I used to email myself my homework so that I could print it out, say at school. Use Dropbox, and I can skip the email part completely.
I remember once going to a lab, but forgetting about bringing the required code. Not a problem, because it's right there, saved on my Dropbox.
Having things on the cloud, even if it's not cloud storage like Dropbox, is ridiculously useful.
I am very organized, and I have a lot of space on my Dropbox, so I save, name and date all of my school work, side projects, and other random useful things that I might need. It's so convenient having them on the Dropbox folder, because now they appear on all the computers that I use. And everytime I make a change on one computer, all the other computers will be guaranteed to have the same change.
I use Dropbox to complement GitHub. While I like the idea of GitHub, the downtime between pushing a change and fetching it on a new computer is a bit too high. Since my projects aren't that large, I can use Dropbox along with it. I synchronize all my project files so that wherever I am and whichever computer I'm using, I can still commit some changes to the project. It's a bit faster, though it means I don't get to use Git as much.
Actually, this system caused me a bit of trouble when I almost deleted my entire website. I was learning and trying out a lot of new stuff for the new site, but I hadn't committed any changes. Then I did some weird things, and all of my new changes were deleted. I didn't want to roll back and start all over, so I panicked.
It turns out I was saved by Dropbox, since the web application keeps a track of recent changes. So I could go on the site and recover all the files I lost. It was basically a life saver, so every few days I thank Dropbox for its services, and still kind of marvel at how amazing the idea is.