Developer: Michael Taylor
Price: free Download on the App Store
Briefcase Lite seeks to turn your iPhone into a briefcase for your docs (not that anyone keeps large files in briefcases all that much anymore, but that is for another day). But you will need to wait for an update or the full version if you want to give this app a try. There is a bug that is preventing the lite version of Briefcase from viewing docs; which essentially renders the app useless.
In the full version you have a similar syncing system as other apps - you create a shared connection over Wi-Fi to your computer and synchronize files. You will have to use port forwarding in order to get your computer visible on a network for file transfer (a similar process must be done on a Mac, though it is less steps). Either way, this only works as a functional solution if you have a high amount of tech knowledge.
Best to look at other apps or services if you do not want to put in too much time to computer tinkering for Briefcase Lite to work.