As is often the case, many of the best and most memorable events in the rivalry have been goals—either the spectacular, the perfectly timed or both.
Let's look at 10 of the best from some of the premier matches England has to offer.
We begin with Cristiano Ronaldo exemplifying what makes him a unique player.
Could anyone else in the world have netted a free-kick from about 40 yards out on the right flank? I doubt it.
Manchester United would go on to beat Arsenal in that year's Champions League semifinal and take care of Chelsea to win the whole thing.
I'm not sure whether the goal or Ryan Giggs' brawny chest hair makes this moment more famous.
The goal, at least, was classic Giggs. At the peak of his physical power, he had searing pace and could use his technical skills at full sprint to beat defenders. He does so brilliantly here against one of the greatest defenses ever assembled.
After he scores, he removes his shirt in elation, reminding us that the 1990s was quite a different era of style.
OK, this one isn't a goal, but the fact that it was not a goal has etched it into the lore of the Arsenal-Manchester United rivalry.
With Arsenal's unbeaten record on the line, United earned a penalty in the dying seconds. Ruud van Nistelrooy stepped up to take it.
As fate would have it, he smashed his shot into the crossbar and left all of Old Trafford in disbelief.
Martin Keown, who conceded the penalty, did not miss the opportunity to remind van Nistelrooy of his miss immediately afterward.
Eighteen-year-old Serge Gnabry recently scored his first goal for Arsenal against Swansea City. If he knows about Nicolas Anelka's first goal for the club at the same age, he'll be able to put it in perspective.
In the season that would see the young Anelka become a force, he netted his first goal out of absolutely nothing at Highbury against Manchester United.
The Red Devils should not have given him nearly as much space to shoot, but it took serious confidence for the youngster to try to beat Peter Schmeichel at the near post from the edge of the penalty box.
You want to talk about confidence? Take a look at the goal that epitomized Freddie Ljungberg's red-haired days.
Obviously, very little thought went into this goal—he simply saw the ball, instinctively knew to chip it over the goalkeeper and married supreme confidence with excellent technical ability to do so.
This was Ljungberg and Arsenal at both of their swashbuckling bests.
Disclaimer: This will not be Thierry Henry's only appearance on this list.
Thierry Henry is not known for his cranial goalscoring proficiency, but one of the best moments of his career came via the noggin.
In Arsenal's first season at the Emirates and Henry's last during his first spell at the club, the oft-injured Frenchman did not have many moments to savor.
But, like all truly great athletes, he managed to muster one moment of brilliance against an old foe.
Edwin van der Sar was powerless to stop Henry from grabbing all three points for Arsenal that day.
Lost in the abject humiliation Arsenal suffered during their infamous 8-2 drubbing at Old Trafford were some really outstanding goals.
Almost every one was remarkable in its own right, but my personal favorite is Ashley Young's delicious curler to take the score to 2-0. He takes only one step before bending the ball all the way around Wojciech Szczesny and nestling it in the very top corner of the net.
Say what you will about Young's tendency to dive or his other footballing characteristics, but any player who can do this is one of real quality.
In one of the most famous FA Cup finals ever, Alan Sunderland nicked the trophy for Arsenal in the very last seconds of the game.
There was perhaps more drama in this final than in any of its predecessors or successors. The Gunners looked to be coasting to victory with a 2-0 lead and 85 minutes gone. But Manchester United scored two goals in three minutes to shockingly equalize.
With extra time seemingly in the cards, a classic Liam Brady run eventually produced a cross for the gloriously 'fro-ed Alan Sunderland at the far post, and the rest is history.
I've always thought of this goal as the classic case of a player simply taking the game into his own hands (or feet, as it were).
With no one contesting him for a loose ball following Ray Parlour's corner kick, Patrick Vieira simply said "Alright, this is mine now," and venomously blasted a curling screamer past the goalkeeper, off the crossbar and in.
It's certainly one of the highlights of Vieira's illustrious career, and a moment when he truly became a vital cog in Arsenal's most successful sides.
The Frenchman's statue outside the Emirates depicts him after scoring a stunning individual goal against Tottenham, but this might be the best of his career.
And he made it look so incredibly easy.
Confidence, circumstance and utterly extraordinary skill converged in one serendipitous moment at Highbury to produce a gem that must have left every fan in the stadium gasping for air.