Airplanes falling from the sky at midnight, nuclear meltdowns, stock market collapses -- those were just some of the calamities that were supposed to befall civilization as a result of the Y2K Bug. The glitch stemmed from the fact that most computer programs before the turn of the century used only two digits to represent the year. So experts assumed that when 1999 became 2000, many of the systems that run critical infrastructure would be tricked into believing we were back in 1900 and freak out. It turned out not much happened. Whether that was due to the billions of dollars spent on systems remediation, or to Y2K being mostly hype, is still the subject of ongoing debate.
Further reading: IT Hall Of Shame, Part 1