Discover is the only free app in the whole App store that gives you the full functionality of a wireless hard disk. With just a wireless network, you can freely upload/download files to your iPhone.
You can either use the WebDAV protocol to connect to your iPhone via Finder, Windows Explorer or Nautilus (Gnome) or use the Web interface and connect to it via your browser. If you are a Windows user, there is even a Discover Windows client that you can use to connect to your iPhone.
Discover comes with several useful features. There is an iPhone-discovery mode where you can discover other iPhones in your network and share files with them. There is also a viewer within the app that enables you to view your files while on the move.
Briefcase Lite is the free alternative to the paid app Briefcase. This free app allows you to connect your iPhone to Mac and Linux in a local area network environment (Windows is not supported). Similar to Discovery, you can transfer files to/from your iPhone and there is a viewer to view the various type of files while on the move.
There are several limitations to Briefcase Lite compared to Briefcase. Firstly, you can only upload files, but not directories. This means that if you have plenty of files, you have to upload them one by one, rather than upload them as one folder. Secondly, Briefcase Lite does not come with the remote login feature that is available in Briefcase. Thirdly, Briefcase Lite does not allow you to send files to another iPhone, but you can receive files from a Briefcase user.
In general, if you want basic file transfer and viewing functions, Briefcase Lite is sufficient. If you are looking for more sophisticated features like remote login and remote mounting of disk images and installing of packages, then Briefcase is the one to go.
Free Third Party Software
Other than the apps at the app store which deal on the iPhone side, there are also several third-party software that focus mainly on the computer side. You only need to install these software in your Windows and you will be able to browse, transfer and control your iPhone via the USB cable. There are several software for Mac as well but they are paid apps, so I will not mention them here.
iPhoneBrowser is a Windows based file browser for your iPhone. Once you have it installed in your Windows, you can navigate the whole iPhone filesystem and drag and drop files to it. You can also perform backups in case you accidentally delete some important files.
Same as iPhonebrowser, DiskAid is another software that allows you to browse and transfer files to your iPhone. There are lesser options, but it has a far simpler interface and easy to understand icons.
If you have jailbroken your iPhone, there are some useful applications in the Cydia app that you can use.
Installing Netatalk via the Cydia app gives you the ability to connect your iPhone to your Mac using the AFP protocol. You can access your iPhone via the Finder and drag and drop any files to it.
OpenSSH may not be the most elegant way to connect to your iPhone, but it is the best and easiest way for you to tweak and hack your iPhone. You will need a SSH client on your computer to make use of OpenSSH. Cyberduck (Mac), WinSCP (Windows) and Filezilla (Linux) are a few great SSH clients that you can use.
With OpenSSH, not only can you transfer files to/from your iPhone, you can also move the internal files around (do it at your own risk) or change the file permissions. This is useful if you are looking to hack your phone and install any cracked applications.
The above mentioned applications are some of the free alternatives to turn your iPhone into an external hard disk. Surely there are many more ways/hacks that you can use to access your iPhone, some of them are paid apps and are not mentioned here. If you use any of those, do share them with us.