Retrieve Voice Memos from device?

If you look in the iPhone user manual - in the section on Voice Memos (Chapter 28, page 105) - it walks you through the intended process for syncing with your computer.

http://manuals.info.apple.com/en_US/iphone_user_guide.pdf

Sharing voice memos with your computer

You can sync voice memos with the primary iTunes library on your computer, then listen to memos on your computer or sync them with another iPhone or iPod touch.

When you delete a synced memo from iTunes, it stays on the device where it was recorded, but is deleted from any other iPhone or iPod touch you synced. If you delete a synced memo on iPhone, it's copied back to iPhone the next time you sync with iTunes, but you can’t sync that copy back to iTunes a second time.

Sync voice memos with iTunes: Connect iPhone to your computer, then in iTunes select iPhone. Select Music at the top of the screen (between Apps and Movies), select Sync Music, select “Include voice memos,” and click Apply.

Voice memos synced from iPhone to your computer appear in the Music list and in the Voice Memos playlist in iTunes. Memos synced from your computer appear in the Voice Memos app on iPhone, but not in the Music app

iTunes should actually sync Voice Memos if you have the option 'Sync Voice Memos' checked in the 'Music' tab when the iOS device is connected (either through USB or Wifi).

I actually forgot I had this item checked in iTunes, and noticed I had a new playlist named 'Voice Memos' in iTunes. These were rather short (only a minute to 5 long I think), but synced ok.

If you delete a Voice Memo from the iTunes Library, it will not be deleted from the device on which it was recorded, as stated by the Manual, the next time that device is synced. In fact when you re-sync that device again, it is possible to have that Memo (which had been deleted from the iTunes Library on the computer) be copied back again into the iTunes Library on the computer, by checking the Include Voice Memos on the Device/Settings/Music page (as of iTunes 12.11.0.26).

Additionally, if the iTunes Library on the computer is empty at the time you connect a device on which some memos have been recorded, these memos will not be erased on the device when you sync; on the contrary, they will be copied back to the iTunes Library on the computer, no matter if Include Voice Memos is checked or not on the Device/Settings/Music page. Do not be deterred by the warning message in iTunes :

This iTunes library is empty. If you link the iPhone [device name] to this library, all songs on the iPhone will be erased. Are you sure you want to continue?

as this will not apply to the Voice Memos which were recorded on the device (as of iTunes 12.11.0.26).

This answer by jmlumpkin is canonically correct, all existing memos sync over to a special "Voice Memos" playlist in iTunes. However, if you like to record voice memos that you will retrieve later on your computer, my suggestion would be to check out DropVox. Instead of having to go through iTunes, DropVox uploads your recordings to your DropBox folder as soon as you finish recording, which for me is far more convenient than syncing and dealing with iTunes. Personally, I have completely dropped Voice Memos and now completely use DropVox for everything.

Another avenue to avoid iTunes but still use the Voice Memo app is to use a software package like PhoneView to grab your existing memos directly from the device.

There is a free third-party utility that I find very useful in situations like this. Macroplant 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.

You can extract the voice memos from your iPhone back up by downloading this free application: http://www.iclarified.com/entry/index.php?enid=4974 This will allow you to read the files from your back up files. (saved my life) The site also walks you through how to use it - it's really simple. Once you have extracted the IOS files, go to the media folder and you will find recordings. That's where your voice memos will be!

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 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.