Here's my list (sorted in some order)
Major US:
Alaska
America West
American
Continental
Delta
Northwest
Southwest
United
US Air
US Commuters/Shuttles:
American Eagle
ASA
Comair
Delta Shuttle
Skywest
United Express
United Shuttle
Australia/Pacific:
Air New Zealand
Air Pacific
Air Polynesie
Bush Pilots Airways
Connair
McMiller Robinson Airlines
Qantas
... and one more across Fiji; the name escapes me
Other International:
Air France
Aero Mexico
BA
Cathay
Korean
KLM
Lufthansa
Mexicana
Scandinavian
Singapore
Virgin Atlantic
Out of Business:
Air Cal
Airspur Helicopters
Braniff (number 2)
Jet America
Linjeflyg
Pan Am (the original)
PSA
TWA
Western
Business Express
Pacific Express
Pan Am Express
Ansett
TAA
BEA
BOAC
Sabena
Swissair
Swissair Asia