I realize it's a perennial question, but with all the recent discussion of both Brady and Mannings legacies, it's also topical. I also take it for granted whom most here consider the GoAT, and I happen to agree: We can debate whether others had bigger arms, faster feet, clearer vision, quicker releases, sharper minds or more "clutchness," but Elway combined them ALL at equally elite levels. For example, Montana never missed and Marino practically teleported passes, but both were statues in the pocket: Which—if either—was SECOND best?
For the record, choices are listed in order of personal ranking and, no, Favre's NOT there, because he was a pick machine in close games: That's why he only reached two SBs and only won the first. Also, Johnny U arguably SHOULD be there (and I'd fittingly rank him either just ahead of or behind Manning) but most of his best years were pre-merger; by the time he reached SBs, he played both hurt and past his prime, splitting time with Earl Morrall (maybe the best BACKUP QB of the SB era; by SB V Unitas was HIS backup.)
I don't see how Bradshaw keeps sneaking in to these lists, let alone excluding Staubach in the process. Let's not forget there was no David Robinson Rule then, so Staubach spent his first 4 pro years on active duty in the Navy, retired the year of his last passing title, still at the top of his game, and split time with Morton all year when Dallas lost SB V—yet STILL started 4 SBs despite all that, losing only to the Steelers dynasty whose QB Bradshaw was lucky enough to be. Plugging ANY decent QB into a team with Franco Harris, John Stallworth and the Steel Curtain would yield the same result.
Tarkenton scrambled just as much and well as "Roger the Dodger" and was just as accurate and long-armed, but lacked Dallas' offensive support. He was Elway BEFORE Elway, reaching SBs on the Purple People Eaters and his sheer athletic ability despite having NOTHING else on offense except Lynn Swann and Mick Tinglehoff (this years senior HoF finalist.) He retired with every passing record in existence, but NO SB Rings because he had the misfortune of sharing a conference with the Landry dynasty and facing the Steelers dynasty whenever he managed to get past Dallas.
Recalling the '70s competition makes Dallas and/or Pitt reaching 7 SBs in 10 years even more impressive, but Bradshaw was just along for the ride. Brady belongs in his company, but not in a GOOD way.