Tom Brady has the most games by a quarterback with 200+ passing yards, with 244 games.

which qb has the most career games with 200 passing yds
Interpreted as:
Which qb has the most career regular-season games with 200 or more passing yds?
BradyBreesManningFavreRiversRyanRoethlisbergerMarinoRodgersManningStaffordMoonPalmerElwayBledsoeFoutsMontanaTarkentonFlaccoTestaverdeUnitasCollinsMcNabb244238222209196181181179163159154142137137128125117115114114113111109
NAMEGPYDSCMPATTPCTAVGYDS/GTDTD%INTINT%SCKSCKYRATE
Tom BradyTom Brady24472,0146,0419,23365.47.8295.15375.81551.74072,560101.5
Drew BreesDrew Brees23873,0396,3769,30168.67.9306.95295.72122.33552,514101.4
Peyton ManningPeyton Manning22265,2075,4558,25666.17.9293.74996.02102.52621,71399.6
Brett FavreBrett Favre20957,7734,8637,71263.17.5276.44175.42293.03632,37291.5
Philip RiversPhilip Rivers19656,1704,5806,94066.08.1286.63765.41762.53782,26698.3
Matt RyanMatt Ryan18152,5314,5486,85666.37.7290.23244.71442.13722,46896.3
Ben RoethlisbergerBen Roethlisberger18152,5014,3246,62065.37.9290.13385.11592.43912,60696.6
Dan MarinoDan Marino17951,5584,0526,66960.87.7288.03655.51983.02151,50590.8
Aaron RodgersAaron Rodgers16347,4173,8595,87065.78.1290.93886.6751.33872,539107.2
Eli ManningEli Manning15945,0463,7676,00162.87.5283.32884.81752.92751,95989.5
Matthew StaffordMatthew Stafford15444,5963,7865,98263.37.5289.62884.81392.33442,28392.3
Warren MoonWarren Moon14240,2913,1785,26960.37.6283.72384.51623.13132,25486.5
Carson PalmerCarson Palmer13739,4993,2665,09364.17.8288.32464.81362.72591,78392.8
John ElwayJohn Elway13737,1392,8474,75459.97.8271.12405.01272.72922,19690.2
Drew BledsoeDrew Bledsoe12834,7532,8874,88559.17.1271.52044.21342.73142,13883.5
Dan FoutsDan Fouts12536,1782,7244,49260.68.1289.42245.01844.185.7
Joe MontanaJoe Montana11732,7982,6564,08365.18.0280.32265.51022.597.8
Fran TarkentonFran Tarkenton11529,1652,1213,51460.48.3253.62256.41263.693.4
Joe FlaccoJoe Flacco11431,3122,7564,33363.67.2274.71744.0841.92341,71490.5
Vinny TestaverdeVinny Testaverde11431,1232,4374,15558.77.5273.01864.51513.62181,57981.9
Johnny UnitasJohnny Unitas11329,7931,9603,42457.28.7263.72226.51484.389.6
Kerry CollinsKerry Collins11129,8042,4044,11758.47.2268.51634.01192.92181,44182.1
Donovan McNabbDonovan McNabb10929,9752,4173,93761.47.6275.01944.9782.02721,75993.1
Tony RomoTony Romo10831,1862,5443,84066.38.1288.82245.8982.62131,43999.9
Russell WilsonRussell Wilson10528,0202,2533,35667.18.3266.92176.5591.82821,807107.0
StatMuse has game-level data for passing yards going back to the 1950 season.