Computers were still coming configured with 256 colors as recently as 1997 (or thereabouts -- based on memory rather than research). The web-safe pallette was based on the 216 colors that were common across PC and Mac (as the other 40 were not).
Last time I designed a site in web-safe colors was 1998 but I kept checking with my PC in 256 until some time in 1999/2000.
If I remember correctly Windows 95 first installed with a default 256 colors (16 in safe mode), Windows 98 was the first to default to 16bit.
Anyways, it's certainly old news and -- apart from for historical reasons -- not something you need to worry about any more. You'll struggle to even find a mobile phone with as few as 216 colors these days.