I think it comes down to how staunch a team's fans are over the years which may not reflect the moment. Kind of like the majority of us in here that never left the Rams over decades of success and frequent failure. Many people are bandwagon fans that "love" a team in the moment but will skitter away once they falter. So based on my own perspective over the years:

* Cowboys
* Steelers
* 49er's
* Packers

In any order you choose.

Footnote: I wore one of my Rams hats the other day at a store and the young cashier asked me "Why the Rams?" I paused and said, "Well, back in 1967 when..." He laughed and said "Oh, okay."