The Mail app itself does it. View the attachment and hit the 'share' arrow in the upper right. Dropbox will be one of the options. I just tried it with an Excel file and Dropbox showed up as a choice.
The one downside is photos and videos, which have to be saved to the camera roll first. Then, you can go to Dropbox and import from the camera roll.
So while I wish that photos would act like other files within mail, it's still possible to get anything from mail to Dropbox.