1. Documents by Readdle (FREE)
This free file management app is compatible with iPhone and iPad. Within the free Documents by Readdle, users can view office documents, PDF files, text files, images, movies, music in its built player. While reading PDF ebooks, users can also add annotations into PDF. It can also help iPhone or iPad users to manage files, such as copy, share, protect files with a private password. Users can also synchronize their files with online cloud servers. If you are looking for an iOS file management tool, this free utility must be one of the best choices.
2. File Manager (FREE)
Designed for both iPhone and iPad, the free version of File Manager is another free file organizing app for iOS device users. It supports viewing office documents, iWorks files, music files and PDF directly in the app. Its file management features include: copy, move, zip, sort, create, email, search files and etc. Based on the free app, users can share files with others via USB cable, Wi-Fi and Bluetooth.
3. FileApp (FREE)
Another file management app which works on iPhone and iPad. This free version of FileApp has a beautiful and user-friendly user interface which stands out other free apps. With this free app, users can view documents, PDF, images, videos on iPhone. The supported file management actions include: email, delete, create, edit, zip, move, copy, rename and etc. Users can use USB cable and Wi-Fi to get files from other devices. The shortcoming is that there is no support of sync with cloud servers.
Except these free iOS file managers, there are many paid file managers in Apple store, such as Air Sharing, Awesome Files, Dropcopy, iFiles, iFile Pocket and etc. Among these tools, I've used the iFile Pocket which is designed with both great UI and powerful features: http://itunes.apple.com/us/app/ifile-pocket/id690442933?mt=8.

Main Features of iOS File Manager - iFile Pocket
iFile Pocket is a clean and powerful app that helps manage and organize files, view almost all types of files directly, sync your files with icould servers, share and transfer files via USB and Wi-Fi, create notes of inserted rich media and other practical functions.
1. Sync with popular could servers: share or download files from many could servers including Dropbox, SkyDrive, GoogleDrive, Box.net and etc.
2. Import files from many resources such as image library, iTunes, shared files, other iOS devices, Mac, PC via Wi-Fi, Bluetooth or USB.
3. View multimedia files quickly: browse MS office documents, iWorks documents, PDF, text, image, video, audio and more file types directly in its integrated players.
4. Manage and organize files easily: with this app, you can do almost all kinds of file management actions such as copy, delete, move, email, rename, add favorite, zip, create, encrypt files or folders, save file as PDF and more operations.
5. Make notes with rich media: different from other notepad, the note feature of iFile Pocket can allow you create notes of embedded rich media like audio, image and map.
6. Other small features: support viewing files in thumbnail mode and list mode, sort files by Date, Size, Name or Type, search files, protect files...
It is definitely an ideal iOS file manager choice for anyone. It works perfectly with iOS 5.0 or later version. The iFile Pocket is now only $0.99, temporarily dropped from $3.99 to $0.99. If you need an iOS file manager, iFile Pocket is the best choice for your iOS device.