In 1964 IBM announced one of the most famous mainframes ever, the IBM System/360 which, on the low end versions ran at 0.0018 to 0.034 MIPS. For the time, that was serious performance ... in comparison, the iMac I'm writing this on runs at 92,100 MIPS.
There are, according to Wikipedia, no System/360s known to be still operational despite IBM having leased thousands of them over the product's life.
Thanks to Miles Baska for pointing out the video.
This story, "Historical computing: The launch of the IBM System/360" was originally published by Network World.