It's ridiculous that it takes a third-party app to be able to send a full-resolution video that you recorded on your iPhone without having it be automatically resized to an ugly, low-quality version, but TransferBigFiles does the job.
TBF is a free app, and you get 5GB of storage by default to do what you want. You can send images or video to anyone with an email—which means yourself—at "HD", medium, low and VGA sizes. And, people can send you files to your phone as well, to your "Dropbox", which doesn't mean the Dropbox service.
What's super annoying, and kind of a product killer, is that for some reason, TBF won't let you send files without agreeing to location services. Why does a file transfer app need to know where you are? I have no idea. But if I turn off the location for this—which I did—it refuses to let me pick photos or videos from my library. Please fix this.
In all, the app is not a horrible solution, but it's a solution to a problem that shouldn't exist in the first place. You should have the ability to email files, full size, no matter how big they are. I don't need to be patronized on my own device, please. [iTunes]
Update: A-ha! There's a reason why TransferBigFiles won't work unless you give them permission: It's a rule. iOS doesn't give you access to photos or videos that have location information on them unless you explicitly grant the application location permission. It's a roundabout safety feature, and TBF says they don't use any location info on the user, so it should be safe to switch it on.