Backing up your files
Dropbox is especially good for backing up your files online, although the biggest barriers to this are the size of your backups. You get 2GB free with Dropbox, or you can choose 100GB, 200GB, or 500GB with a monthly fee. There are also business plans that start at 1TB for five users. You'll just have to make sure that the files you want backed up live in the Dropbox folder.
The only issue I have with Dropbox is the somewhat limited amount of free space -- 2GB, but by completing various actions, I was able to get more. You can get up to 18GB by completing tasks such as sharing the app with a friend, adding photos for the first time, and sharing a folder with multiple people. Yes, it provides incentive to learn the various features in the app, but I still think the lower limit should be higher to begin with. It's hard to criticize Dropbox when the app is free, but I would have liked a higher beginning limit (such as 5GB, which is pretty common among the other cloud-storage offerings).
New look and new features
In the latest version of Dropbox, a redesigned interface favors white space and flatter icons, much like Apple's redesign in iOS 7. In addition to the cleaner new look, you can now reorder your favorites folder with touch-and-drag gestures so you can keep frequently accessed files handy at the top. The app also now remembers recent locations when importing files so you don't have to keep digging down through folders. These aren't huge changes to the app, but each update to Dropbox seems to make it even easier to use.
Overall, Dropbox gives you a lot of useful features for free, has a remarkably smooth interface and is easy to use. The redesign of the app makes it look even cleaner, and added features every update continue to keep Dropbox relevant even in a crowded cloud-storage category.
Though it only gives you 2GB of free storage to begin with (along with several tiers of paid storage space), it also lets you complete goals within the app that simultaneously advertise the app to other users while adding space to your storage total. Once these challenges are completed, you'll end up with much more than what most of the biggest competitors offer.
If you find yourself frequently transferring files between different people and computers by hand (via email, USB drives, or other methods), Dropbox is an excellent option with intuitive controls that make the process easy.