Our House - Madness (Seems to be set in the indeterminate past, somewhere in the middle of the 20th century)
Queen - Heaven for Everyone uses vintage footage from Georges Méliès (late 19th/early 20th century filmmaker).
John Fogerty - Centerfield features clips of baseball greats from the '50s.
Rod Stewart - Forever Young is set in what looks to be the 1950s.
Don Henley - The End of the Innocence is another 1950s-looking video.
How about 3.5 billion years or so? 
Yes, for those familiar with the age of the universe, the age of the Earth, and evolution, the video is wildly off in its stated timeline, but is otherwise great: Fatboy Slim - Right Here, Right Now.
I’ve seen at least one really amazingly good K-pop video that’s set in the Korean war, with the lead characters killing each other in the end. It was very powerful, but I have no idea what it’s called.
At the time when I saw it, my friends and I were total anime otaku, accustomed to the Japanese habit of having no idea how to hold a gun in a music video, so it was a total shock. (My dad, for what it’s worth, fought in the Korean war.)
Some films use historical footgage.
Paul Hardcastle’s Nineteen uses news footage of the Vietnam War.
John Fogerty’s “Centerfield” has historical baseball footage.
Gypsy by Fleetwood Mac is set mostly in the 1930’s, and uses some brief newreel footage from the Depression.
That video actually says 350 billion years ago. and judging from the countdown in the corner, primates first appeared circa 35 BYA, homo erectus about 10 BYA and homo sapiens around 1600 CE.
It’s cute, though the Guinness “Evolution” ad is way cooler.
Yup, that’s why I said that the stated timeline in the video was wildly inaccurate. I imposed my own date on the video, since 3.5 BYA is about when the last universal common ancestor is believed to have existed.
Somewhat similarly, Mark Wills’ “19 Somethin’” (recorded in 2002) shows what look like typical home movies from the 70s and 80s, featuring elements of pop culture from those decades.