1983
Completely one-sided for Edmonton, which outscored Calgary 35 to 13 (that means the average score in each game was 7-2 or 7-3 Edmonton). Calgary managed to win game four at home (the final NHL game ever at the Corral)... but only barely, blowing a 6-2 lead with ten minutes left and ending 6-5.
My favorite stat of this era: In this short series, Flames' Dman Paul Reinhart scored 6 (!) goals (in five games)... and went -14.
A great series to see the peak of the cocky, young Oilers going all out and pouring on the offence to humiliate their opponent, but not great for competitive hockey.
1984
I'm not as familiar with this series as I should be and have only seen random clips of games, incl. most of game 7.
Oilers had a 3-1 series lead and probably should have wrapped it up in five, but Grant Fuhr and Gretzky / Kurri all had poor game five's at home, leading to a game six at the Saddledome. Flames had the lead in that one, too, before the Oil tied it in the third and sent it to overtime. But Lanny McDonald scored on a slapper that banked off a body and Fuhr's leg and in. So, game 7.
Back in Edmonton, the Flames enjoyed a 4-3 lead with 26 minutes left on the clock. But the Oil scored three goals in just over four minutes late in the 2nd, which pretty much put it to bed.
The significance of this series was that Calgary showed it wasn't a doormat, as in the previous two seasons, and now was going to challenge Edmonton. (Though they would still get spanked in the regular season for another two years.)
1986
This (and 1991) are the two real classics, I think. This also went to seven games, and, of course remains the only series the Flames ever won vs. Edmonton.
Very good hockey in this series, and lots of great players at their peaks or coming into them. The story of this series is Calgary's disciplined play which didn't give Edmonton the fast-break turnover chances they were accustomed to getting. The other story is how successful the Flames were at Northlands: The Oilers failed to win ANY of their four home games in regulation, losing three of them. And generally, mid-dynasty, the Oil were almost unbeatable at Northlands, so that was very shocking.
Edmonton faced elimination in game six at Calgary... but came up with a very championship-like effort, overcoming an 0-2 deficit to effectively win 3-2 (it was eventually 5-2 but the last two were final-minute goals). It was a heroic third-period Gretzky-to-Coffey-to-Anderson goal that stood up as the winner. Coffey had a strong game, which he generally didn't in this series.
Game 7... Gretzky and Coffey cross signals on the PP, leading to a Flames break that goes in for a shortie. In the 2nd, brutal coverage by Coffey-Huddy allows Peplinksi to go to the net and bang-in his own rebound. The Oil then woke up and scored twice to tie it before the intermission, including a spectacular Kurri-to-Messier breakaway in the final minute (Gretzky and Kurri were broken up as Kurri wasn't scoring).
So, we're at 2-2 heading into the third period, and the Oilers have the momentum. What could go wrong?? (We all know what went wrong.)
But I'm fairly certain that if not for that fluke winner, the Flames win this series anyway. Edmonton was behind the 8-ball from the opening minute of game one and never really recovered.
1988
This is the old-days one I remember best. I was 12, and this was big-time stuff in Alberta back then. Most people predicted a Flames (1st overall that year, and 1st in offense) victory. Calgary had home ice advantage for the first time, and had gone 10-4-2 vs. Edmonton since the 1986 series. But...
The Oilers showed their championship-mettle in this series, being extremely prepared, having a strategy that worked, and playing solid defense. Game one was basically a defensive game, but Kurri broke through (past Reinhart, who had been rushed back from injury and did not look good) to score the game winner. Gretzky clinched it on a breakaway, but this one was a goalies' battle, won by Fuhr. In game two, the Flames broke out to a 2-0 lead and seemed destined to win. They led 4-3 midway through the third period when -- again -- Kurri blew past Reinhart to score and tie it. In overtime, Messier almost won the game but then took a penalty instead in frustration. Fortunately, the second-unit PK was Gretzky-Kurri and they combined again, with Wayne racing down the wing to score on that famous slapshot heard 'round Alberta. Mike Vernon later said he had nightmares about this goal for years afterwards, as everyone knew the series was over the moment it went in. (In fact, Gretzky actually told the Flames' zamboni driver not to bother getting it ready in preparation for a game five.)
Oilers won game three at home, and in game four the fans had the brooms out for the sweep. The Oil built a 4-0 lead before the Flames battled back a bit, but it was far too late.
It was actually a closer series (three of four games were tight) than it appears as a sweep, but nevertheless the Oilers won in four.
1991
This series (along with that Toronto - NY Islanders series from 2002) is the bloodiest, most vicious / brutal hockey series I've ever seen. Just out-of-control, nastiness on almost every shift. Pure hatred between the clubs. By today's standards, nearly every player would have spent literally half the series in the penalty box, with multiple suspensions every game, and probably at least a few lawsuits. Good Lord, it was brutal.
(Examples: That famous Messier elbow to Rick Nattress' head. No penalty called on it. After a Flames' goal, Roberts celebrated a little too much in the goal-crease and was punched hard in the face by Beukeboom, in full view of the ref who was nearby and clearly watching. No penalty.)
Anyway, the Oilers won game one and later won both games at Edmonton to take a 3-1 series lead. But (like in 1984) the Flames fought back and later won game six at Northlands in overtime on the oft-remember Fleury celebration when he basically mocked the Edmonton bench... a bad move, as it turned out.
Game 7 was a classic Flames' choke from this era. A 3-0 lead in the 1st period... and they blew it. First, "Hall of Famer" (choke!) Mike Vernon let in a soft slapper from the boards by Tikkanen, and then Anderson, Tikkanen (again), and Semenov (who was quite a good player) scored. But Calgary tied it in the third and off to overtime we went.
Tikkanen was really fired up in this game, and deservedly he fired home the winner.
2022
I really enjoyed this... only had to wait 31 years. The series featured worse goaltending than any of the 1980s' series had, and there were goals galore. Flames won 9-6 in game one, but actually blew a 6-2 lead before rallying.
Flames had a 2-0 lead and a 3-1 lead in game two... but, you guessed it, they blew it. When Hyman scored shorthanded to break a 3-3 tie in the third period, I knew the Oilers were going to win this series because the look on his face was pure passionate joy, and it was clear the Oilers wanted this more than the Flames did.
The series turned for good in game three with Edmonton winning convincingly, and they won again in game four (despite Mike Smith almost blowing it by letting in a 135-foot flip shot that tied the game in the third). Oilers got a little lucky with a disallowed goal by Calgary late in game five, but in overtime McDavid put it away.
Draisaitl scored 17 points in the five games -- most in NHL history for a five game series.