The world didn't end last Friday just like the world didn't end in the year 2000, with failing computers deleting bank accounts and crashing airplanes. That doesn't mean the world isn't going to end. It will. And if we keep our current operating systems, this is the exact date when all goes poof: 15:30:08 UTC on December 4th of the Year of Our Lord 292,277,026,596.
That's when "the Unix time stamp will exceed the largest value that can be held in a signed 64-bit integer." Unix is what powers most of the computing systems that are vital for human life on Earth, from banks to medical life support systems to electric grids to satellites to the internet. And your iPhone and Android phone too.
Of course, none of the crap today will ever reach the year 292,277,026,596. Not because you forgot to put on that stupid case on your phone but because Earth may not be around by then. The Sun would have destroyed it about 7,900,000,000 years from now. That's when our home star will reach its maximum diameter as a Red Giant, destroying Mercury, Venus and, most probably, Earth.