Eagles went to four in a row as well, from 2001-04.
What's always been weird to me is how, since about 2000, it's felt like the NFC has a lot more parity from year to year than the AFC. Maybe it was just Patriots fatigue, but for the longest time it felt like we were stuck in a Patriots-Steelers-Ravens-Broncos circle jerk in the AFC championship game. Now the faces are finally changing, but the Chiefs have replaced the Patriots and the Bengals and Bills have filled the other spots in the circle.
The Packers and 49ers have played in 11 of the last 13 NFC championship games, but they've only faced each other once and it seems like that second spot has been more of a rotation than in the AFC. There's usually one team that seems to jump up out of nowhere to get this far (Bucs, Rams, Eagles, Lions the past four years).
Of course, then I looked at the actual numbers and there isn't much difference. Eleven NFC teams have reached the championship game since 2014. Thanks to the changing of the guard the past few years, the AFC has had 10. So maybe I'm just an idiot.