I just recently learned of the Year 2038 Problem, a software bug (similar to the infamous Y2K bug) in which many computers can't handle the date properly past a certain range. At its core, it's simply a limitation of 32-bit system architecture and the format in which timestamps are stored. In a nutshell:

The latest time that can be represented in Unix's signed 32-bit integer time format is 03:14:07 UTC on Tuesday, 19 January 2038. Times beyond that will wrap around and be stored internally as a negative number, which these systems will interpret as having occurred on 13 December 1901 rather than 19 January 2038.

So, there we go! There are a number of possible solutions and we've, seemingly, got plenty of time to get there but it's still interesting that it exists.

Vaguely related, there's a time crisis in Japan as well, that comes much sooner than 2038.