I found the solution from madrivergirl was the one that worked for me. The folder will be in the My Pictures>Camera Roll folder if you're using a PC. Copying any random pic file to that folder suddenly let me start viewing my Camera Roll. Several other solutions I found might be helpful to other people with this issue.
One potential solution that worked for me temporarily is to go on your iPhone in Settings>General>Reset and click Reset Location & Privacy. This will of course cause you to be prompted to confirm permissions in almost all your iOS apps again. But it also seems to solve the problem.
Of course powering off and on your phone and your computer can also help.
Another less likely possibility is that the computer does not have the Apple Mobile Support program installed or it needs resetting. Restart the Apple Mobile Device Service (AMDS) on Windows - Apple Support This utility is automatically installed with iTunes.