Navy mugs do not have handles because the idea of the Navy was to create a thick walled mug which was heavy but didn't have a handle which could break off when it slid around and knocked into something such as on rocking ships.
In the early 1940s the U.S. Navy had sent out a request for bids to U.S. companies who could make a coffee mug that would be able to withstand the test of rocking ships.
Mugs with handles would break off when the slid into things on the ship so it was better to have mugs without handles on Navy ships.
Also navy sailors have also been known to not wash their coffee mugs due to bad luck or because the dirty mug is a sign of seniority or because they believe the coffee tastes better in the dirty mug than it does in a clean mug.