Just for grins - what is it? Mr. Athena works on systems that have been in place since the mid-eighties (the company he contracts with just never got around to upgrading it, and it still does the job as long as Mr. Athena is there to love it and comfort it as needed). There has to be something older than that - does anyone know? Is there some molding behemoth in the bottom of the IRS or Census Bureau, still counting away because it does it’s job adequately?
Well, surely there are still some old mainframes floating around.
As for desktop types, when I worked for the Coast Guard they still used CTOS (Convergent Technologies Operating System) machines on an x.25 network. They were phased out almost completely by 2001. This hardware (and software) was circa 1981. They probably sold the hardware to some 3rd world country.
I just left a job in which the manuals were dated from the mid-80’s with one going back to 1982. Stuff like VMS running on a VAX, with COBOL code working on a 1032 backend, if that makes any sense to you.
I couldn’t stand it and left after just a few months.
We still have an old PDP-11 from the 70’s, so I’ve at least got you beat. Its main use is to read the old antique (now obsolete) tapes from very old customer systems so that we can get their old applications when we upgrade them to a new system. We have another PDP whose only purpose in life is to provide spare parts to the one we keep running. You can’t go to the local computer store and buy PDP parts. 
We also have a number of vaxes. Most of those are from the 80’s. For those that don’t know, PDPs (a Programmable Data Processor, so called because “computer” was a really huge thing built by the likes of IBM and required a staff of a dozen just to keep it operating) were the first off the shelf computers, and the predecessors to the vax. Off the shelf back then wasn’t quite like unpacking it and plugging it in like a modern PC, by the way.
I think my companies OS is PONG 1.0
Based on the speed of the damn system in here, I think it might really be Vacuum Tubes 2.3
I adore my 64. 
I’d be willing to wager the circa 1970 computer hardware running the US air traffic control system(s) for the FAA is probably among the oldest hardware still in active and productive use.
There’s a type of lottery in Britain called “Premium Bonds”. As far as I know, ERNIE the computer is still being used to pick the winning numbers; he dates back to around the mid 1950s.
The flight data subsystem and digital 8-track on Voyagers I and II, launched in 1977, are getting pretty long in the tooth. If they’re not already the oldest in use, they likely will be by the time they finish their extended mission in ~2020.
Oh, I thought I was the only former Wachovia employee around here. 
In the Kimberly Clark Plants around here, there are some PDP 9’s running automation on some paper making machines. I am sure in industrial automation, there are many computers dating back from the 70s and 80s.
In the UK at least (don’t know about anywhere else!) T.V’s come equiped with Teletext. This is a news service that is accessed a little bit like the internet. The server that this is run on is obviously ancient. The gfx are terrible, and i’m sure that they haven’t changed since when it first started around about 25 years ago according to this link.
(Hijack) I once tried to describe teletext to some Americans and found it surprisingly hard to do. They have teletext in mainland Europe; I think that it can’t work in America because of the lower number of horizontal lines on TVs there, or something.
Has the INS even discovered computing yet?
Ehm - the graphics are as good as they’ll ever be within the limitations of the media, it has nothing to do with the computer handling it.
Each screenful of teletext is transferred in a signal analogous to what is used to carry just two lines of pixels for a TV picture - it’s essentially a PAL control channel being utilized.
Obviously, that 's not a lot of transmission capacity, and the computer on the other end of that very thin pipe is not the limiting factor on the graphics.
It’s a quite ingenious hack, IMHO.
How about phone switches? Stored program switches were introduced in the late 60’s, and given the way telephone equipment is depreciated (over very long intervals), I wouldn’t be surprised if there was some number 1 ESS machines out there somewhere, happily switching your phone calls. I’m sure some of the early PBX processors of the same vintage are still operating.
The processors used in those early switches qualified as generic computing machines, though the architecture was proprietary, and typically had some wierd instructions which catered to switching applications (like strange bit manipulation instructions which acted on mass data indexed in strange ways). Programmers in a particular environment also typically made use of microcoded instructions aimed at really speeding up things like handling bit maps representing phone line status for a particular product, etc. Early in my career, I coded in EPL, the structured assembler for Bell Labs switches (PBX, not CO). I don’t go far enough back to have had to use the non-structured assembler which preceded it, thank god. Non-power-of-two data bus size, BTW. 24 bit, IIRC.