The disaster we worried about "most" or "the most"?

You can say either "the disaster we worried about most was a nuclear war" or "the disaster we worried about the most was a nuclear war". Both are acceptable.

Using "most" by itself means it's more worrisome more than other disasters, but leaves it open to the possibility that there might be a more worrisome disaster that just wasn't thought of.

Using "the most" implies that it is the absolute number one worst disaster possible.