The following two apps need root access to your phone and will not work on a standard user access only phone.
These applications do require a basic knowledge of file sharing structures.

Application: Samba Filesharing
Restrictions: Device MUST be rooted*.
Price: Free
Store Link: Samba Filesharing available on Google Play
Description: Samba Filesharing allows you to access your Android SDcard on the network. On a Windows PC this is seen as a computer network share with access to the folders and files on it. The Android device hosting the Samba Filesharing app effectively becomes a file server. This means other network devices can connect and watch videos, listen to music or view OpenOffice/Doc documents and etc. One can use Samba FileSharing and WiFi tethering as a file server for other Android devices like the Sony XPERIA U (4GB) which don't have the storage, but one can still stream and watch a movie or just share files.
Comments: AirDroid gives many of the file access features of Samba Filesharing within a web browser, but Samba Filesharing allows full access to all file media types if the remote host application support them. For example mkv, vob and OpenOffice documents and etc can be opened without file downloads to your device to view them(where supported).

Application: CifsManager
Restrictions: Device MUST be rooted*.
Price: Free
Store Link: CifsManager available on Google Play
Description: Allows remote NAS/File server shares to be mounted locally on your Android device and seen as local files/folders.
Comments: This is the next step up in file sharing as this allows your Android device to access remote files as if they were local to that Android device. This has many benefits for example if one has an OpenOffice document, it can be opened on both the Android device or any other device with access to the NAS/file server on which it resides. Documents and files which would otherwise have to be downloaded to be accessed, can be access by the Android device from the source device without copies being created.
This application is not for the faint hearted as it may require a supporting cifs.ko module for the application to work and this may not be readily available for your Android device/OS version.
* A rooted device is an Android device with full access to read and write to all system files and not just user files.