The "betrayal" of former 49er Charles Haley going to Dallas, or former Cowboy Ken Norton, Jr. making the same move to San Francisco only heightened the hated rivalry.
It certainly isn't the oldest or, perhaps, even the best. One could make the argument that the Packers-Bears is the best of all time. Hailing from the West Coast, I enjoyed the myriad of rivalries from the Oakland Raiders perspective, including against the Broncos and Chiefs.
However, the 49ers-Cowboys rivalry was the one that I believe helped transform the NFL into America's Game.