Dynasties can have different definitions. Is it the org or a group of individuals? How long do they last? What is "excellence" or "dominance" mean? For the sake of trying to define it, the Ming Dynasty and the Roman Empire each lasted hundreds of years and had multiple leaders. The common thread is that the organizational structure stayed relatively constant. For the sake of discussion, I will define as dynasty as a franchise having a consistent pattern of excellence for an extended period of time. Like the Ming D and Roman E., they lost a battle every now and then but when they were always a power.
For sports that is not the NFL, I am book-ending the dynasty eras with championships or championship appearances
From 1921 to 1964 Yankees played in 29 World Series and won 20 of them.
From 1953 to 1979, the Canadiens played in 19 Stanley Cup finals and won 16 of them.
From 1957 to 1969, the Celtics played in 12 NBA Finals and won 11 championships.
Football. This is hard. IMO there are four teams that are in the discussion. 49ers, Pats, Steelers and Cowboys(?). For the sake of argument, I'm trying to create an apples-to-apples comparison.
49ers: 1980-2002 (22 years) 5 SB appearances. 5 titles. 9 NFCCG appearances. 18 playoff appearances. 49ers had various coaches but the Yorks (Eddie, Denise, Jed) owned the team and Walsh - and his system were around for the most part (coach & GM). From 2003 to 2010 the 49ers were a mess. I will not include 2011-2014. Even though the Yorks still own the team, I am excluding Yankees in the latter 60s and afterwards and Canadiens after 1979.
Patriots: 1994 to 2014 (20 years) 7 SB appearances. 4 titles. 9 AFCCG appearances. 16 playoff appearances. Kraft has been there. BB was there in 1996. Drew was there in 1996 and 2001. TB of course from 2000 on..
Steelers: 1972 to 2014 (42 years) 8 SB appearances. 6 SB titles. 14 AFCCG appearances. 27 playoff appearances. Rooneys are the only constant. The Steelers need to be in the discussion b/c they have the most titles. Obviously when compared to Pats and 49ers, they have had almost 2X amount of time to accumulate the numbers.
Cowboys: 1966 to 1995 (30 years) 16 NFCCG appearances, 5 SB, 8 SB appearances and 23 playoff appearances. Strong trend of winning but without a common denominator as they have had different owners, coaches, etc. not sure the term "dynasty" applies.
Giants: 1981-2011 (30 years) 4 SB. 5 SB appearances. 5 NFCCG appearances. 15 playoff appearances. The Mara family is the constant. Pats and 49ers have done more in less time.
It was fun to do this. Not sure what the right answer is..