|The Post och Inrikes Tidningar was founded in 1645|
and switched to an online-only format on January 1, 2007
Back in August I wrote about a pair of Japanese inns that have each been in continuous operation for well over 1,000 years, now Oddee has a list of its 10 oldest companies still in business (which includes one of those hotels).
These businesses range from restaurants and pubs to a construction company, newspaper, and firearms manufacturer.
Any of these would make a great backdrop or plot point for a game that involved characters with extended lifespans (e.g. Vampire: The Masquerade) or access to time travel (e.g. the Doctor Who RPG).