Yes, R-tree turned out to be a godsend when working with larger geospatial data and calculating intersections.

Yep, that's what I used it for! Intersections. Hard to make concurrent though. Ended up with concurrent map backed geohash.

I've used quadtrees for some cool stuff I can't really talk about. All the things you think binary trees are good at but with x,y coordinates, or any n-tuple of coordinates as you suggest.

Also LSM trees!