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 Transfer Big Files does the job.
Transfer Big Files 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 Transfer Big Files 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 patronised 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 Transfer Big Files says they don't use any location info on the user, so it should be safe to switch it on.