NATO, known as OTAN in French, was an organization existing on Earth during the early 21st century.
During one of its meetings, George W. Bush and Tony Blair shook hands. In 2154, after Jonathan Archer restored a damaged timeline, this meeting could be seen in the time stream as the timeline realigned itself. (ENT: "Storm Front, Part II")
NATO stands for North Atlantic Treaty Organization. It was never mentioned in dialogue, but its name can be seen in the background of the Bush-Blair meeting. The photograph seems to have been taken on 21 November 2002, as part of the Prague summit, at the Hilton hotel in Prague.
The first draft script of "VOY: "Death Wish"" had, instead of Thaddius Riker, an unnamed great, great grandfather of Geordi La Forge who was a pilot for the NATO Air Force during the Albanian Incursion in 2011.
Terms from the NATO phonetic alphabet are used in the names of stations such as Science Station Tango Sierra, authorization codes, and planet names such as Alfa 177.