A couple of often mentioned offline video player apps are AVPlayer and OPlayer. They have a variety of methods you can use for downloading videos, including DropBox. I have no idea what the best option is, or even which or the best. OPlayer does what I need it to do on the rare occasions I need it; so I stopped looking.
Though, as Johanna said, you can play videos from Dropbox when offline, if you favorite them first (while you are online) and wait for them to finish downloading. I you don't need a lot of features, and only occasionally play videos offline, it may be good enough.