1) Hunt prolongs Everton's wait (Everton 2–2 Liverpool, First Division, Sept 1962)

Everton were relegated for only the second time in their history in 1951. Now, we're going off piste immediately this week, and that's because they gurgled down the swannee in some style. Needing a draw at fellow strugglers Sheffield Wednesday to ensure their safety, they somehow conspired to lose 6-0. All the sympathy that day was with Wednesday, who also went down, on goal average behind Chelsea, who pipped them by winning their last four games of the season. The Guardian's "Old International", Donny Davies, averted his eyes from the plight of the terrible Toffees, noting only that "to abuse Everton at this stage would be too much like picking up a person badly mauled from a street accident and reading him a lecture on the folly of jay-walking".

Anyway, Everton's relegation meant there wouldn't be a Merseyside derby in the league for 11 seasons. Everton took three campaigns to get back up to the top flight, but their successful promotion season coincided with Liverpool slipping down a division, the Reds embarking on an eight-season spell in the Second. There was a fourth-round FA Cup tie at Goodison in 1955, Billy Liddell, Alan A'Court and John Evans (twice) scoring for Liverpool in a 4-0 shock, but as for the league, it would be a long wait.

All that milling about was finally over in 1962, when Bill Shankly finally took the club back up. A Goodison crowd of 73,000 – a Goodison crowd of seventy-three thousand – prepared themselves for a treat. "When the teams came out, the tension was undoubtedly high," reported the Guardian, "but it is pleasing to record that throughout the citizens of Liverpool conducted themselves admirably. No bottles were thrown, no stones, no orange peel, and for once even the goalmouths were not bestrewn with plebeian toilet paper. True, Liverpool's senior mascot at one point was pelted with apples, but that is one of the hazards of excessive loyalty."

The game was a blinder: four goals, a disputed penalty, two disallowed efforts, and a late equaliser. Everton could have been 2-0 up within five minutes. In the opening 60 seconds, Liverpool's goalkeeper Jim Furnell dropped a cross under pressure from Roy Vernon, who drove the ball home. The referee gave the keeper a dubious benefit of the doubt. Dennis Stevens put the ball in the Liverpool net again four minutes later, but was ruled offside.

Everton finally went ahead after 27 minutes, though there was more controversy, Gerry Byrne wrongly accused of handling the ball in the area, Vernon scoring from the spot. But on 38 minutes Kevin Lewis converted an Ian Callaghan cross to equalise. Everton went ahead again on 63 minutes, the former Liverpool winger Johnny Morrissey scoring, but they would be denied at the death by Roger Hunt, who scrambled home with less than 60 seconds to go. Everton had waited 11 years since their last victory over Liverpool – a 2-0 win at Anfield in that relegation season – and they would have to wait a little longer yet. (The return match at Anfield would end goalless.) Still, winning the league championship at the end of the season probably took the edge off.

2) Brown's goal of the season (Everton 0–3 Liverpool, First Division, December 1969)

Both teams recorded their first league victories over each other in Liverpool's championship season of 1963-64, the Reds winning 2-1 at Anfield, Everton returning the result with interest, 3-1 at Goodison. The next two seasons saw a couple of almighty shellackings, games that probably stand as the results of the decade. In September 1964, the deposed champs Everton went to the home of their newly crowned rivals, and made a landgrab for local pride: propelled relentlessly forward by Alex Young and a youthful Colin Harvey, they were 3-0 up by half-time, and ended up 4-0 winners. It was Everton's biggest win over Liverpool since the first world war was in full swing, a 5-0 tonking in 1914. Liverpool refused to take that lying down; in the same fixture the following season, they hammered Everton 5-0, four goals coming in the second half, Roger Hunt their chief tormentor.

Great results, great matches, yet the quintessential 1960s Mersey derby moment came in the very final meeting of the decade between the two old rivals. After winning 15 of their first 18 games in the 1969-70 season, Harry Catterick's side were clear favourites for the title: nearest challengers Leeds had managed only eight wins by that point. But Everton stumbled a little around Christmas and the New Year, allowing Leeds to catch up. This was the most symbolic game of that stutter, a 3-0 Goodison skelping at the hands of Liverpool, who were already leading through an Emlyn Hughes header when it happened.

On 54 minutes, the left-back Sandy Brown sent perhaps the cleanest, crispest diving header in the history of All Football past his own keeper Gordon West and into the top corner of the net from 10 yards out. "He must wish the ground would open up," screamed commentator David Coleman famously, as the BBC cameras captured the Merseyside derby in full glorious colour for the first time. Bobby Graham made it three, Ian Ross should have made it four but ballooned over from close range, but the real damage had been done.

Liverpool had hauled themselves into the title race with the victory, but the result was no harbinger. Shankly's ageing side were too inconsistent – they would crash out of the FA Cup at the quarter-final stage to second-division strugglers Watford, a result that convinced Shanks to break up his first great team – while Everton regrouped in the New Year and held off Leeds to win their second title under Catterick.

3) Thomas rules out Hamilton's winner (Everton 2–2 Liverpool, FA Cup, April 1977)

Ten days after losing a marathon League Cup final replay to Aston Villa, Everton came out with renewed vigour in the semi-final of England's other cup competition. Not that Gordon Lee's side needed much in the way of geeing up: the opposition was Liverpool, who were closing in on a treble of league, FA Cup and European Cup. And Everton were surely due one: since winning 1-0 at Goodison in November 1971, they'd failed to beat Liverpool in 10 games. They'd also failed to score in the first eight of those, a period that lasted a month shy of five years. (In fairness, that run of results also included four goalless draws on the bounce, but nonetheless at least Liverpool bookended those games with 1-0 victories, scoring at a heady rate of just over 0.33 goals per match.) When Martin Dobson finally scored against the Reds in October 1976, a fine 25-yard swerver, Liverpool were already two up, and on their way to a 3-1 win. Yes, it's fair to say that statistically at the very least, Everton were due one.

They didn't get one, though they should have. The game at Maine Road was a tumultuous affair. Terry McDermott opened the scoring with the BBC goal of the season, hip-shaking exquisitely past Mick Buckley, shifting the ball to his left with his right heel, then lifting a gorgeous chip over David Lawson from the edge of the area. Duncan McKenzie equalised, the teams level at half time. With 17 minutes to go, Jimmy Case headed Liverpool back in front, but McKenzie refused to let it lie, powering down the inside-right channel, his weaving run drawing the entire Liverpool defence out to him. Having pulled Liverpool to ribbons, he crossed low for Bruce Rioch to tap home.

And then the moment still guaranteed to send Everton fans of a certain age into orbit. Three minutes from the end, a superb reverse pass down the left wing sent Ronnie Goodlass scampering into space. He dropped a shoulder and powered past Case, clipping a cross towards the near post for McKenzie, who stooped to flick on for Bryan Hamilton. Hamilton guided the ball into the bottom-right corner of the goal with his front tail, Ray Clemence wincing in agony at the jig being up for Liverpool. But the referee Clive Thomas came to Liverpool's aid, chalking the goal up for – well, what, exactly? Thomas has never explained his decision, initially thought to be for hand ball, but later assumed to be for offside. Replays conclusively show that either decision would be palpably wrong. Liverpool went on to win the replay, but not the cup. Still, a league and European Cup double wasn't to be sniffed at, one game short of a historic treble, in the days when you had to win the title first in order to give it a shot.

4) King deposes Liverpool (Everton 1–0 Liverpool, First Division, October 1978)

A moment of high comedy. Everton finally beat Liverpool again during the early exchanges of the 1978-79 season, Andy King hitting a scorching drive into the top-right corner at Goodison, the goal enough to secure his side's first Merseyside win in seven years. Evertonians went wild at the final whistle, cavorting across the pitch as Liverpool slunk off to the changing rooms. But one man of the red persuasion remained on the prowl, and would ensure this fixture would remain in the memory for more than one reason.

As the Everton fans danced around him, BBC North West Tonight's Richard Duckenfield held a microphone under the nose of the hero of the hour. Fixing the camera with a cheesy grin, Duckenfield was finally given his cue to start the interview. "Andy King …" he began, at which point, with exquisite comic timing, a police officer hoved into view from stage right, barging King and Duckenfield down the nearby player's tunnel. "Can you get off the pitch!" barked the copper, clearly smarting from the result, his wee dictatorial eyes rapidly narrowing like pissholes in quicksand. "Come on! Get off the pitch!" To King and Duckenfield's eternal credit, both men took this eejit's promptings in good humour.

Everton went unbeaten in their first 19 games of that season, but couldn't shake off Bob Paisley's side, who were always in the box seat. No wonder, as that Liverpool team was probably Anfield's greatest vintage of all, despite the modern trend for awarding that title to the 1987-88 team.

5) Sheedy salutes the Kop (Liverpool 3–1 Everton, First Division, April 1987)

Everton were hoping to effectively seal the First Division title at Anfield: a win would have taken them nine points and at least 16 goals clear of Liverpool, who would have only had three matches left to play. Kenny Dalglish's side weren't going to go down without a fight, though, and ran out 3-1 winners, ensuring at least that the outgoing champions wouldn't have to hand over their title on their own patch.

Ian Rush scored twice, therefore equalling Dixie Dean's record of 19 in Merseyside derbies. (He would go on to break that, finally totalling 25 against the team he supported as a child.) But the most memorable goal of the game, for more than one reason, was scored by Kevin Sheedy. On its own terms, his rocket free-kick, which arrowed into the top-left corner of the net, would have gone down in folklore. But it was Sheedy's celebration that really stuck in the memory, the former Liverpool player running in front of the Kop flicking the Vs, then giving the Kemlyn Road stand some as well.

The Kop, as you'd imagine, went ballistic. But then, in a sign of how infantilised modern society has becomes, instead of whelping at police and stewards because the bad man did a rude thing, the fans started to laugh. "Despite crossing the great Mersey divide I'd always got on well with the Liverpool fans," said Sheedy years later. "They were always fine with me. Without sounding big-headed, I think they recognised me as a good player and respected me for that. It was not like I'd walked out of Anfield as a high-profile player in controversial circumstances and I think the fact Liverpool were enjoying so much success at the time must have helped.

"I can honestly say now, though, that it was just a spur of the moment reaction and I wasn't being disrespectful. To this day, I still don't know what made me do it. It wasn't something I planned and it wasn't meant to cause offence because there was also a fair number of Evertonians on the Kop that day."

Sheedy was rapped on the knuckles by the FA, but it was all soon forgotten, and 99% forgiven as well. But imagine the bleating if Steven Gerrard pulls off this trick at Goodison on Saturday. State of football today.

6) Westerveld's late let-off (Everton 0–0 Liverpool, Premier League April 2000)

A terrible Mersey derby, but what an ending. Deep into injury time, Sander Westerveld hit a free-kick upfield, surely the moment that would see the referee Graham Poll put the final whistle to his lips. But Westerveld foolishly clanked the clearance straight into the back of the retreating Don Hutchison, the ball ballooning back past the open-mouthed Liverpool keeper and into the empty net. The winner.

Only it wasn't, because Poll disallowed the goal and immediately called time, ostentatiously pointing at his watch as a sea of livid blue-shirted players engulfed him. Graham Poll: the poor man's Clive Thomas? Perhaps, though at least Poll did explain himself afterwards. "As the goalkeeper kicked the ball I blew for time, but in the confusion, in the noise, no one heard the whistle."

The fact that there were still 15 seconds of injury time to play was a subject not broached, though Poll also argued that Hutchison had failed to move back the mandatory 10 yards, hence his decision to disallow the goal. Which had been scored, er, after Poll claimed the match had already finished. At which point Poll chalked it off, then blew his whistle for full time again. Still, this sort of confusion at the end of a game only happens once in a lifetime, doesn't it?

For a Joy of Six on the best Merseyside derby games, rather then moments, click here.

Thanks to Gary Naylor.