All deserve their fine reputations. It's pretty much impossible to compare eras, but they all have compelling cases in very different ways.
But what about Joe Root? For Root has now led England to victory in 23 Tests including his last six in succession. One more victory will draw him level with Alastair Cook (who captained England 59 times) and Andrew Strauss (50) and put him just two behind Michael Vaughan, who led England to victory in a record 26 Tests (51).
This Test at the Ageas Bowl will be Root's 43rd as captain. Which means his win percentage - 54.76 - is better than any of them. If England win again, it will be the longest win sequence for an England captain since Percy Chapman in 1930. Sounds pretty good, doesn't it?
Ultimately, captains probably aren't judged on such stats. Not entirely, anyway. The changing pace of modern cricket has resulted in fewer draws so, impressive though Root's win percentage as leader may be (higher than Clive Lloyd's, Imran Khan's, MS Dhoni's and Michael Clarke's, among many others), his loss percentage is also high. At 35.71, it's higher (far higher in some cases) than any of those mentioned other than Cook.
To be remembered as a great captain, it's probably necessary to be involved in a specific, high-profile series victory. And, for England captains, that probably has to include away wins in Australia or India. Root's reputation will hinge on how England fare in India (or the UAE, as seems likely) this winter and in Australia the year after. If he can regain the Ashes in an away series, his reputation will be assured.
It's worth reflecting on Brearley's record a little here. Excellent though it is - he never lost a home Test as captain - it should be remembered that he never captained against the great West Indies side of the era. Equally, his record in Ashes encounters - not least the 5-1 Ashes victory of 1978-79 - was inflated by a number of World Series defections.
Brearley averaged 16.72 in that series; his overall average as England captain was 22.48. There's no way that could be tolerated now. And can you imagine the social media reactions if Root had been involved in a 129-run stand in the World Cup final that occupied 38-and-a-half overs, as Brearley was in 1979?
The point of this is not to decry Brearley's outstanding record. It's to show how time lends a veneer to reputations. How history tends to see characters in black and white. Brearley returned to Australia as captain in 1979-80. England lost 3-0 but the Ashes weren't on the line so it tends to get overlooked. In England, anyway.
Right now, we're able to see Root's imperfections. We're able to look at him bowling himself after lunch on the second day of the previous Test and criticise him for his lack of tactical awareness. It allowed Pakistan to thrash 27 quick runs and dissipated all the pressure built in the morning session; in a low-scoring match, it could have been pivotal. "I don't think I had a very good game last week to be honest," Root said on Wednesday. "I think I made a few tactical errors."
But nobody will recall such minor details in 20 years' time. They'll remember who won the Ashes and who ended up as the leading run-scorer in England's Test and ODI history. Root has every chance of achieving both.
We surely judge captains far too much on the tactical side of the job. Look at Cook: while he rarely showed much tactical flair, he led admirably in other ways. With the bat, for example, he made six centuries in his first 14 innings as England's Test captain, while perhaps his best work was conducted ahead of that India tour of 2012 in persuading his team-mates - and the coach, Andy Flower - to accept the return of Kevin Pietersen. That took monumental powers of persuasion which were rewarded as England won. It's a result that seems more miraculous with each passing year.
One area Root hasn't made progress is with his own batting. And that matters, as it's still the role in which he is most likely to shape games. Dropping back down to No. 4 may help but tempo appears to be his issue. Desperate to lead by example, he seems to be fighting his natural, positive inclinations in demonstrating that he can play in an attritional manner. One century in 15 Tests - and that on a flat wicket in Hamilton - is a poor return for one so talented. It's an area he needs - and England need - to improve.
But there really aren't many other options. Root really is the one automatic selection in all conditions who definitely wants the job.
Yes, Stokes could do it. He could probably keep wicket, too, if he was asked. But he's already developed into the key batsman, bowler and fielder in all three formats of the game. Do England really want to burden him with more responsibility just as he is fulfilling his promise? There is no evidence at all that he is looking to take on the role; quite the opposite, in fact. Root has his complete support.
Maybe, in time, Rory Burns will emerge as a candidate - he's already led Surrey to the County Championship, after all. But he needs to cement his place - and his natural authority - with a spell of heavy run-scoring first. Let's see how he's doing after the Ashes.
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Root will miss Stokes in Southampton. Not just as a player - that goes without saying - but as a trusted confidante and lieutenant. Remember Stokes rounding on Stuart Broad in Centurion after Broad had appeared to disagree with Root's tactics? There may be times when Root misses that supportive, enforcing voice.
That's not to imply Root is weak. Anyone can shout and rave, but it takes a bit more strength to remain calm and constructive under pressure; to appear in front of TV cameras at moments of great triumph and despair and manage to be magnanimous and frank.
"I wouldn't say I give the hairdryer treatment but when we've not performed well you have to make people aware," he said. "But there's no point doing that without giving a solution - that's the most important thing. We want to be a solutions-based team."
Let's remember, too, the reputation of the England team not so long ago. It's not just that they were unpopular with their opponents; they didn't even seem to much like each other. Remember the Sri Lankan players rounding on Root in Leeds in 2014? Or the Jadeja incident at Trent Bridge a few weeks later? Remember the tit-for-tat articles and books that ruined the reputation of the England side which went to No. 1 in the Test rankings?
Root inherited all that. Yet he's formed a team spirit that seems genuinely united with a shared purpose that has already weather some significant disappointments and embraced some significant successes.
Under Root (and, to be fair, Eoin Morgan and Cook), this England side has embraced its wider responsibilities to the game. Every selfie request is accepted, every autograph signed. Just as importantly, they seem genuinely committed to one another, enjoying each other's successes and supporting them through the failures. Root deserves a lot of credit for creating that environment. It's probably the key role of a captain.
So it's Root or bust for England in the next 18 months. And while the jury is still out on his overall reputation - rightly or wrongly, this side is building to the 2021-22 Ashes series which will define him - his record is rather better than is sometimes suggested.
There's a lot to like about this Root-led England side; let's not make the mistake of judging it by comparisons to history's unreliable memory.