Going to have to call out Detroit. The amount of times Quebec and Detroit have had to face off in important playoff games, are too many to just bury the hatchet. Quite a few brushings with them late 60's early 70's.
Both teams were consistent cup contenders but the only time we both ended up in a final together Quebec took the W without too much hassle.
We have had quite a history of running into each other even in earlier rounds. You know anytime it's a Detroit v Quebec playoff round you are in for a great series.

The expansion and playoff restructure of S76 has led to the likelihood of Quebec and Detroit running into each other way less likely. It is likely a new rivalry is going to emerge soon and so far Kelowna is looking like the most likely.
Quebec ran over Kelowna during Quebec's latest cup run and a few seasons later Kelowna returned the favor steamrolling Quebec early to go on a win a cup themselves.

While the likely new chapter of rivalries is being written, let's not forget the old ones with Deotrit. Should we see a Detroit vs Quebec finals the rivalry might just be ignited full blaze again.