Spuckbeutel Air Sickness bags
  Airlines T
 
TAA -  Trans Australia, Melbourne, Australia, 1946 - 1986 renamed as Australian Airlines.

TAAG, Luanda, Angola, founded 1938 as DTA, renamed 1975.
  #2,    - with thanks to Gerd Clemens  -   #5      and    #6:

TABAN Air, Teheran, Iran, founded 2006.    -  #2,             #5 :

TACA, San Salvador, El Salvador, founded 1931.  #1, and -with thanks to Steve Silberberg-  #2a:

TACV Cabo Verde Airlines,  Praia, Cape Verde, founded 1958.
#1,     #2,    and  -with thanks to Thorsten Hecht  #5,  - to Dr. David Bradford -  #6:

TAE Trabajos Aereos y Enlaces, Madrid, Spain, 1967 - 1982.   -    #1  and  #2:

TAESA, Mexico-City, 1988-2000.    -#1                       and     #3:

Tajik Air, Dushanbe, Tajikistan, founded 2007 by renaming from Tajikistan Airlines.  #1:

TAM Transporte Aereo Militar, La Paz, Bolivia, founded 1945.  -  #1:

TAM, Sao Paulo, Brazil,  founded 1961. -  
#1,               #5/#18/#26/#27/#28(small variations),             #20              and           #23:

#11,                                               #3,                                         and     #2:

TAM Mercosur, Asuncion, Paraguay, founded 1996. 
               #6,                    #21(smaller bag, different base),           #16 :

TAME (Transportes Aereos Militares Ecuatorianos), Quito, Ecuador, founded 1962, since 1970 civil air transport.
#17,                         #22,                             #13,                     and                 #31:

TAP Air Portugal, Lisbon, founded 1945.   -    #30,          #28,      and       #6:

-      #2/#3/#10(small variations,            #17           and               #29/#29a:

#32/#32a,                         #34              and   #36(print both sides)/#37(print front only):

Tara Air, Kathmandu, Nepal, founded 2009, subsidary of Yeti  Air(q.v.).
#1 / #2 (color shade variation):

TAROM, Bucarest, Romania, founded 1954.
 #3(normal-)/#6(glossy paper),              #4,                #5,                      #12:

              #16,                       #8,                          #1                  and           #7:       

TEA Switzerland, Basel, 1988-1999. 
Founded by spin off of TEA Group Belgium and disappeared by being integrated to Easy Jet. - #2:

Texas International, Houston, USA, 1947-1982 merged into Continental (q.v.).    - #1:

THAI Airways, Bangkok, founded 1960.  #1,       #18             and              #27:

 #24(glossy)/#31(normal paper),  #25(glossy)/#20(normal paper and diff. maker),  #13a  and  #10: