Almost every airline I've flown has already been mentioned.
Not mentioned:
In the mid 80s, there was something called Air Atlanta. All the seats were First Class, at an economy price. We flew it to Orlando and back, connecting in Atlanta. It only lasted a few years.
BWIA (British West Indies Airlines)-New York to Barbados. Now defunct.
Sabena (Belgian Airlines)-New York to Brussels. Now defunct.
Still flying and already mentioned: Air New Zealand. However, I did NOT fly to NZ, but rather from Los Angeles to London and back. Before I took these flights, I didn't realize flying between two countries using a third country's airline was legal, but I learned there is something called "Fifth Freedom" flights where it is possible. The flight originates in Auckland, stops in LA, then continues to London.