Latest version of Word for ios supports dropbox.
iCab uploading files
"FILE UPLOADS:iCab Mobile can upload any files on web pages, like uploading photos on flickr.com or Facebook.com. Due to limitations of the iOS this does not everywhere, but it works fine on many web sites."
https://itunes.apple.com/us/app/icab-mobile-web-browser/id308111628?mt=8
See this thread.
https://discussions.apple.com/thread/2714162?tstart=0
email the file to some email you have like gmail. Use icab to access your email on the web. download. upload to site.
iUploader app
"The iUploader app is the only way I know of to load files such as resumes and cover letters to sites such as Monster and CareerBuilder (those having the "Browse for File" links intended for desktop use) from an iOS device. If there is another way to do it, then I'm just not aware of it. I asked for this on the Apple discussion forum months ago and now here it is! Thank you app devs for this!" https://itunes.apple.com/us/app/iuploader-free-uploads-downloads/id541315293?mt= 8
I know some or one of these apps will support dropbox.
All of the "Office" document editing applications on the iPad have limitations. Best try them out to see if they meet your needs.
Free apps
Apple iWork
iWork by Apple -- free with newly purchased iPads
http://www.imore.com/how-get-all-iwork-apps-iphoto-and-imovie-free-eligible-ipho ne-or-ipad
iWork for iCloud Beta
https://www.apple.com/iwork-for-icloud/
Citrix ShareFile QuickEdit
"Is the simplest document-editing tool available for iOS devices. Open, view, create and edit Microsoft® Word, Excel® and PowerPoint® files — right from your iPod®, iPhone® or iPad®!" Was Office² HD.
https://itunes.apple.com/gb/app/id364361728?mt=8
Kingsoft Office
"Read, edit PowerPoint files, and read Word documents on your iPhone or iPad, Share it by cloud storage."
http://www.kingsoftstore.com/office-free-ios
Microsoft Office
"View, create and edit" Excel, Powerpoint and Word "documents for free! Plus: open, edit and save documents from Dropbox."
https://itunes.apple.com/us/app/microsoft-excel-for-ipad/id586683407?mt=8
https://itunes.apple.com/us/app/microsoft-powerpoint-for-ipad/id586449534?mt=8
https://itunes.apple.com/us/app/microsoft-word-for-ipad/id586447913?mt=8
Google
Docs
"Open, edit, and save Microsoft Word documents. Share documents and work together with others in the same document at the same time."
https://itunes.apple.com/us/app/google-docs/id842842640?mt=8
Sheets
"Open, edit, and save Microsoft Excel files. Share spreadsheets and work together with others in the same spreadsheet at the same time."
https://itunes.apple.com/us/app/google-sheets/id842849113?mt=8
Slides
"Open, edit, and save Microsoft PowerPoint files. Share presentations and work together with others in the same presentation at the same time."
https://itunes.apple.com/app/id879478102
CloudOn
Client front end to a Microsoft Office running on a server
"CloudOn brings Microsoft Office® to your iPhone & iPad and links it to your Box, Dropbox, Google Drive and SkyDrive accounts." Free for a give number of documents.
https://itunes.apple.com/us/app/cloudon/id474025452?mt=8
Paid
DocsToGo
• VIEW/EDIT/CREATE Word & Excel files(Office 2007/2008/2010)
• VIEW PowerPoint, PDF, iWork, Text, .RTF, and more!
• Send & receive attached supported documents using the built-in Mail app
• FREE desktop application with your purchase! Compatible on Win & Mac allows you 2-way file sync with a WIFI connection.
• Open & Edit files within DocsToGo from any 3rd party app that supports the “Open In” feature
• Supports iTunes File Sharing via USB cable for manually moving files
https://itunes.apple.com/us/app/documents-to-go-office-suite/id317117961?mt=8
Thanks to Texas Mac Man for pointing to this link.
"Quickoffice Connect Mobile Suite and Documents To Go These two apps share an important feature: unlike Numbers, they can open, edit, and save an Excel spreadsheet without stripping out any data or formatting, even though they can’t display or edit all the existing information; spreadsheets can make the round trip from Mac to iPad and back safely, without losing anything."
http://www.macworld.com/article/1159958/ipadspreadsheet.html
Office 365
Office Mobile for iPhone requires a qualifying Office 365 subscription
* Edit - You can make quick edits to Word, Excel and PowerPoint documents.
* Documents Remain Intact - Formatting and content remain intact when you edit Word, Excel, or PowerPoint documents on your phone.
* Edit While Offline - Your device doesn’t have to be continuously connected to the network to work on an Office document that is stored online. You can view and edit recently used documents even while you’re offline. Your changes will be saved online when your device reconnects to the network or to Wi-Fi.
* Create – You can create new Word and Excel documents on your phone.
https://itunes.apple.com/en/app/office-mobile-for-office-365/id541164041?mt=8