Yes you can use dropbox, there's even a wordpress plugin (that's if you're using wordpress) called "WordPress Backup to Dropbox" which makes the whole process a lot easier. But make sure you have enough space in your dropbox account, which could be the main problem as dropbox has limited hosting space.
Restoring your backup can also be a problem, I've seen a lot of complains about this on the wordpress forum and haven't seen any good solution for this issue. So that's the risk. If you have a bigger website then I would advise you to stay away from dropbox backup.
The free plugin doesn't compress files and if you want to create a zip to compress your files you have to upgrade the plugin. I would rather spend my money on another great plugin like BackupBuddy than "WordPress Backup to Dropbox".
So the point is, you can, but it's too risky and not safe especially if you have a bigger website.
