Many, many years ago Washington (National), Tampa, Orlando, Miami on a National 727 then picked up a Pan Am 727 to San Juan, Antigua, Barbados (where the runway lights packed up after landing and we finally departed after they had put out oil lamps along the runway and not many at that) Port of Spain. All in the same direction but a long day compared to what would be possible today.
The other one that sticks in the mind was again all in the right direction but London/Amsterdam, change, Amsterdam/Frankfurt/Rome/Bahrain/Bombay/Bangkok/Jakarta, change, Jakarta/Bali and on the way home Singapore/Kuala Lumpur/Colombo/Karachi/Dubai/Amsterdam change Amsterdam/London.
These days I pay extra to avoid indirect routings!
I was a travel agent around the same time and I booked a seaman to come home from Taipei to London using Pan Am to Tokyo and then BOAC to London. He never appeared. Got on to Pan Am to be told they had rerouted him (without permission) to fly their "RTW" flight (PA002?) which operated Tokyo/Hong Kong/Bangkok/Delhi/Tehran/Beirut/Frankfurt/London instead of Tokyo/Anchorage/London.