It might seem like Dropbox (or other online file syncing and sharing services, like Google Drive or OneDrive), are an ideal backup solution, but a recent horror story of someone losing all their photos on Dropbox is an excellent reminder: You can't rely on just one backup method.
Jan Curn tells his photo disaster story on Medium. After turning on "selective sync" (which is meant to keep files on Dropbox but not on your hard drive) for thousands of her photos and videos to try to save space on her computer, the Dropbox sync client crashed, so he killed the app and restarted his computer. Two months later, he discovered all of those files were permanently deleted and unrecoverable, since Dropbox only keeps files in the recycling bin for 30 days. They were the only copies of years worth of photos.
Dropbox is ideal for syncing files across systems, but because it only keeps deleted files for 30 days, it's not ideal as a backup solution. Other online storage and syncing solutions are similar: It's too easy to make a change in your files that permanently loses your data. You're better off using both a file syncing tool, like Dropbox, and an online backup service, like CrashPlan (which holds on to your files even if your drive is disconnected or it's been deleted from your system).
Practise the 3-2-1 system of backing up and you'll (hopefully) avoid file loss tragedies like Curn sadly is facing.