Not sure how to phrase this question, but I found one routing between DEN and CAY taking something like 45 hours with 5 stops. Let’s say you love aviation so much that you want to buy a ticket that will give you the most stops and take the longest to get to your destination. So what city pairs in the whole world would take the longest, with multiple stops and layovers? Needs to be an actual buy-able ticket.
I went to this planning site and did a Melbourne to Melbourne RTW (Round the World) trips with 8 ‘stops’.
I used Sydney as the second last stop so MEL to SYD was 8 stops, 17 flights (as I chose stops that were not direct flights) and a bit over 5 days.
There was a lot of transit times in airports along the way.
There are many sites such as Pointshack that will help you cheaply reach Gold/Saphire status on Frequent Flyer programs which is good for Lounge Access when you fly.
In 1986 I took a forty hours, multi stop flight from Sydney, Australia to Boston, USA.
Stops in Hawaii(2hrs), LAX(8hrs), Denver(2hrs) and JFK(2hrs).
I can now do the same flight in 20 hours.
I was a student and this was the cheapest fare at the time. A return flight with one stop costs the same today as this one way flight did almost 35 years ago.