One day I am going to abuse myself and put together an LCC/ULCC round-the-world itinerary...just because.
This flight might be cheating though since it's 1 leg instead of 3, so my odds of catastrophic disappointment are drastically lowered.
Thinking Spirit or Frontier from LAX to the East Coast - Norwegian Air Shuttle across the Atlantic - Norwegian to Singapore - TigerAir to Hanoi - VietJet to Seoul - Jin Air to Honolulu - Allegiant to Las Vegas and whatever garbage carrier from Vegas back to LA.