For the past few months I have been using the Speed Software's free (and ad free) Explorer as my file manager. It is a nice powerful, non-frills file manager. Given that it is the sibling of Speed Software's powerful paid app, Root Explorer it has good genes.
I use drop box on my phone to view files that I keep on my Dropbox account, which keeps my files on my two computers and smartphone in sync. I have had no problem uploading pictures and audio files to Dropbox, but when I tried to upload a Word document today, I realized that Dropbox needed different file manager as the Dropbox application for Android did not recognize Explorer.
After searching online, I decided to try OpenIntents OI File Manager. This app is free (and ad free) and will allow you to upload any file to Dropbox from your Android device.