In 1999, Y2K was a big scary thing that everyone was sure was going to destroy the world. Then the new year happened, it was no big deal, and a lot of folks got the idea it was a false alarm. But I have heard from people whose judgment I trust that we only got through Y2K without trouble because of a lot of hard work put in by a lot of programmers and engineers. Was it a close run thing, or did they finish work with time to spare? How close to serious trouble did we come when the calendar turned?
Disaster was unlikely. The biggest risks were probably
Failure of systems giving early warning of missile attack (e.g., by nuclear-armed ICBMs). Significant reduction of risk was simply obtained by being aware of the Y2K risk, and being prepared to not panic. Of course, the computer systems got suitable attention in the prevent-Y2K work. There were no known incidents of this type.
Failure of nuclear reactors. Unlikely to occur, but the consequences of failure could be serious. There were Y2K incidents at nuclear power plants: 15 nuclear power plants had issues, all minor (7 in the USA, 2 or 3 in Japan, 2 in Spain, at least 1 in Russia). Plants were being monitored for problems, and problems could be, and were, quickly responded to. The biggest Y2K-related incident at a nuclear power plant wasn't a Y2K incident in the strict sense, but occurred during pre-2000 testing at Peach Bottom, Pa. - the electronic sensor system crashed and workers used the old-fashioned gauges (retained as a back-up system for safety).
Air traffic control failure or similar failure of control of rail traffic or maritime traffic. Again, these were checked fairly thoroughly, and due attention paid during the Y2K change-of-year. No serious incidents.
Failure of electricity distribution grids. Also checked fairly thoroughly, and due attention paid during the Y2K change-of-year. No serious incidents.
Basically, no disasters. If nothing had been done about these possibilities, disasters were certainly possible, and the effort put into critical systems to ensure no disasters wasn't wasted. Less critical systems received much less attention, and many systems failed. Some air-conditioner control systems failed, some taxi meters failed, some medical equipment failed, some breathalysers (alcohol breath-testing units) failed, some railway ticketing machines failed, and some reports and forms were printed with the wrong dates. These were typical representative problems, and could not be accurately described as disasters.
There were Y2K problems which inconvenienced people, and which even led to deaths. There were various financial errors (the impact of which was much lower because they could be recognised as Y2K errors rather than leading to ongoing disputes between, e.g., banks and customers). The British NHS sent incorrect Down's syndrome test results to 154 pregnant women, with 2 terminations resulting (and 4 babies with Down syndrome being born to women who had been sent incorrect negative test results).
It is estimated that about US$34 billion was spent in the US to prevent/fix Y2K problems, much of this on the less critical systems.
More details in my reply to a Y2K question from a year ago in: More details in my reply from a year ago in https://www.reddit.com/r/AskHistorians/comments/abcfl9/why_did_y2k_kill_my_digital_watch_but_nothing_else/