Despite having lived in 4 different countries on 3 continents, and five different US States, nothing too exotic on my list....

Airlines now gone:
Air Atlanta
America West
ATA
Canadian
Eastern
MarkAir
National
Northwest
Pan Am
PeoplExpress
Piedmont
Reeve Aleutian Airways
Reno Air
Republic Airlines
Trump Shuttle
TWA
Viasa

Airlines still in existence (but some for not too much longer):
Air Canada
Air France
AirTran
Alaska Airlines
American Airlines
British Airways
Continental
Delta
ERA Aviation
Frontier
Frontier Flying Service
Horizon
jetBlue
KLM
Larry's Flying Service
Qantas
South African Airways
Southwest
United
US Airways
Virgin Atlantic