Why AppleTV displays "An error occurred loading this content. Try again later" error?

Solution 1:

If you hold down the Menu button and the down arrow on the remote for 10 sec until the LED on the front of the Apple TV begins to flash. Let go of the buttons and the Apple TV will do a soft reboot.
This has been happening to me several times a week and doing this seems to fix the issue.

Solution 2:

I fixed mine by just going back to the stv menu and trying to play it again.

In my case I was streaming the content from my iPad.

Solution 3:

For my Apple TV 4K, Buddy's answer worked as well, but my remote has no down arrow. I had to reboot the Apple TV by pressing the MENU button and the TV button together for a couple seconds until the LED flashes and TV went dark.

Solution 4:

I think I have fixed the problem. I unplugged the AppleTV and plugged back in (since I could find no way to reboot via the UI, #fail) and now my programs seem to be playing with no problems.

Another odd thing though was that I had to "reboot" a couple of times as it failed to fully load the menus the first two times and the remote was completely unresponsive... It starting to sound like I may have a faulty unit...