That reminds me: the original outline for the TOS episode Mirror, Mirror took place in a parallel universe which was almost exactly the same as the normal one.
(In other words, it wasn't the Always Chaotic Evil Universe we saw on screen.)
The major differences were that McCoy (not Spock) had a beard; Kirk was married; and nobody had ever invented the phaser. Which led to Starfleet nearly being defeated by an alien race who never gave "our" Kirk any trouble.
Of course, when Kirk arrives in this parallel world, he promptly re-invents the phaser and saves the day.
In other words, it was very much a riff on L. Sprague de Camp's Lest Darkness Fall.