This is probably not feasible, but I wonder if they could put one of these under buildings in earthquake-prone areas. It would be like a giant shock absorber for the building.

They do this, sort of. It's called base isolation, and essentially, they put the whole structure on sliding bearings. (They don't do the vertical component, but that's typically not as big of a deal as the shear forces.) It takes some care dealing with utilities and connections to non-base isolated things, but it's quite effective.

It's done for high value structures that have to be functioning through emergencies, like emergency management centers and hospitals.

[edit I can't find documentation for this: I believe that the Bay Bridge has some of the biggest ones ever made, at roughly 9 feet of travel. (Though that was 20 years ago, and may not be current)]