Question: iOS seems to refuse to allow me to email "long" voice memos, and I'm unaware of any way to extract them from iTunes backups of my phone. How can I retrieve entire voice memos that aren't really short?

Answer: 
There is a free third-party utility that I find very useful in situations like this. [Macroplant iExplorer](http://www.macroplant.com/iexplorer/), for Mac and Windows, lets you mount the file system of your iOS device in the Finder or Windows Explorer, so you can copy the voice memo files (and most other iOS document files) directly to your computer without using iTunes. Macroplant also provides other paid apps with additional functionality.
There is an unclear aspect of iTunes which isn't mentioned in the other answers here.

After selecting the iPhone, iTunes (12.1.2.27) shows an *On My Device > Voice Memos* list in the sidebar. However, this list doesn't actually seem to show all the voice memos on the device(!).

In particular, newly recorded memos don't seem to show for me, although they do in the [PhoneView](http://www.ecamm.com/mac/phoneview/) app. Perhaps memos only appear in that list after the device has been synced.

So: don't try and use the *On My Device > Voice Memos* list to retrieve memos from the device. Use the solutions mentioned in the other answers here instead.