A few years ago, I went to a tech demo/hackathon thing. Somebody had some neat experiments with preloading pages speculatively based on user behaviour

The coolest approach given was when a user types in the search box, kick off the request for the full results page if they move their mouse on a motion curve towards one of the results, with some machine learned data on how people move their mouse: Not quite in a straight line, and with some acceleration.