25 years from today, 19 January 2038, at 03:14:08 UTC, an odd thing will happen to some of the no doubt very large number of computing devices in our world: an old, well-known and well-understood bug will cause their calculation of time to fail.
The problem springs from the use of a 32-bit signed integer to store a time value, as a number of seconds since 00:00:00 UTC on Thursday, 1 January 1970, a practice begun in early UNIX systems with the standard C library data structure time_t. On 19 January 2038, at 03:14:08 UTC that integer will overflow, as demonstrated in this animated GIF:
For more detail on the problem, see the Wikipedia article on it. Wikipedia also has an article with an interesting collection of important time formatting and storage bugs, including Year 2038, Y2K, Days 32,768 and 65,536 and Year 10,000 — via redwolf.newsvine.com