The NS Savannah

While many cruisers, aircraft carriers, and submarines have been powered by nuclear reactors since the 1950s, only a handful of civilian ships have ever been powered by the fission of uranium. The first of these was the NS Savannah, a joint project of the Atomic Energy Commission and the US Maritime Administration launched in 1959. You can read more about her here:
NS Savannah

Savannah was officially a cargo-passenger merchant vessel, but looked more like an oil baron's oversized yacht. The exterior was designed to be sleek, pretty, and imposing, the shape of things to come, although it did nothing to help Savannah's economics. In principle moving large amounts of cargo with nuclear power makes sense due to the long-term savings in fuel costs, especially now in the post-peak oil era, but loading and unloading cargo from Savannah's low-drag bow was a pain and the lines limited usable volume. It would've made more sense to use the Babcock & Wilcox reactor's 74 megawatts to plow through the waves with the stubby practical bow typical of true merchant ships, but the AEC let the Maritime Administration get away with a little indulgence for the demonstration project.

Over the years the novelty of moving cargo and passengers with the decay of heavy metal wore off, and when the subsidies dried up in 1972 Savannah was decommissioned. She didn't show that nuclear power was uneconomical for ships, only that it's uneconomical when combined with impractical design choices. After all, the Soviets and Russians have found much to like running their icebreakers on nuclear energy, and I suspect that this is an idea whose time will come again, when the era of cheap oil oozing from the ground is a fading memory. Until we go back to that future, we'll have the newsreels to remind us of what it was like there: