Once jet engines became reliable enough to trust (ie be certified) only two vs three/four engine configurations - it was all over for the super jumbos. The graph above clearly demonstrates the fuel/pay load differentials.
I first flew on a 747 (Pan Am) in the mid-70s as a young teen on my first trip to Europe. We left out of SFO, and had to land in Labrador to re-fuel in order to reach Heathrow. I've been fortunate to be able to travel to many places in the world, and have traveled on 747s to/from Asia, as well as 380s to/from Europe.
In fact, 380s take so long to board that once when we were connecting from Rome through DeGaul and were delayed through customs (non EU have passport control when leaving) that we almost missed our flight. We thought we were the last ones to board, but the plane sat for another 1/2 hour as more people and more supplies continued to be loaded. They literally take hours to prep, load and fly.
As so many posters above have already pointed out, it's just easier on airports, passengers, crew and maintenance to fly mid-range planes with two engines. They are more flexible, more fuel efficient, and more comfortable for passengers.
Whether it's Boeing's Dreamliner 787 (flew that to Greece last fall), or Airbus' 320 line up (countless times), this is where the industry is headed - actually, already there.
ETOPS certainly killed the 4 engine Jumbo.. but that’s the funny thing about the 380... ETOPS already existed when they designed the thing... Unlike the 747 which was built when you had to have 3+ engines to be able to fly transoceanic .
The 380 didn’t need 4 engines to fly the distances, it needed the 4 engines to fly the weight and number of passengers.
I would like to actually fly a 747 before they are fully retired, but I honestly doubt I will get the opportunity. I don’t fly often and rarely long haul. Not that a 747 would be the experience it was when they first flew... can you imagine an airplane with a lounge/bar?