First, login to your Dropbox account and get the "share link" for one of your files.
Then, change the front part of that link from
www.dropbox.com
to
dl.dropboxusercontent.com
For example, this URL presents options to download the file
https://www.dropbox.com/s/prk0linsrgoy6o3/hah_plain.txt
While this URL presents the file content directly (if the browser is able to render it)
https://dl.dropboxusercontent.com/s/prk0linsrgoy6o3/hah_plain.txt
This tip is especially useful because Dropbox can directly present movies without requiring the Flash plug-in. Which means an iPod, iPhone, or iPad can still view those files (as long as they're set up properly in the first place).
Or what about a computer without Flash? I intentionally don't have it installed--not at the system level anyway [I gotta document my install process]. However, Safari or Firefox on my computer can still display the following video (possibly NSFW: "it's not crack or nuthin', but it's still really bad").
https://dl.dropboxusercontent.com/s/m4yygo4p5okhxlj/Vertical_Video_Syndrome-A_PSA.mp4
(original at http://www.youtube.com/watch?v=Bt9zSfinwFA)
Also, [all this Flash stuff should be its own post, but] for an install-less Flash setup on your computer, just download Chrome (thank you, Pepper).
Still haven't gotten your own free Dropbox? Use my referral! We'll both get additional free storage!