An interesting topic. Bit of recency and Ashes bias but I guess that was always likely - could argue for others but that ten seem all well justified for the short list.
I reckon I am fairly qualified to opine on some of these having been in the stands for all the Melbourne Tests (except the Typhoon Tyson one - that was a bit early even for me)
Sort of depends on what you mean by "greatest" , no ? If it is principally "overwhelming " you are after , then 2010/11 wins at a canter. (Though Gatting's mob had a similarly easy win back in 86/87 - not on the list). When a team bowls Australia out , at home , for under 100 on day one and steams past without losing a wicket before close of play you would be hard pressed to find anything to top it. And that Australian team wasn't exactly bereft of decent players : Ponting , Clarke , Hussey ...reckons they'd all get a game today. Even had Steve Smith
But if you are after excitement it's hard to go past that Headley-inspired effort in 1998. (Yes I know 1982 was the closest finish : but honestly for most of that match I felt England were a shade on top and it wasn't until that extraordinary last wicket stand of Border and Thompson almost stole the result that it became nervy - very nervy !)
1998 though was up and down throughout and Australia definitely held the upper hand going into the last day...in fact they almost certainly thought it was in the bag when they cleaned up the England second innings despite some amusing tail end swipes from the generally incompetent Mullally annoying the hell out of Glen McGrath
Must admit I didn't fancy England's chances of defending 160 even when a couple of early wickets went down. The third wicket stand really seemed to have the home side cruising in ...but of course nothing is certain in cricket and once it was broken (and it was a very fine catch by Ramprakash - one of his better acts in an England shirt ! ) and Headley got into his spell of a lifetime the boot was suddenly on the other foot...
With Steve Waugh still at the crease and a couple of wickets left the result was still logically in doubt : but somehow I (and a group of visiting English tourists sitting next to me ) sensed then that it was fated to go one way only ...and at the end of that incredible four hour final session Waugh made the mistake of allowing Darren Gough to have a go at the rabbits...end of story. Cue wild celebrations...only downside was that it wasn't one to bring back the Ashes so I can see why it was not going to be chosen. Still a magic day to be at the MCG
Karachi has to be high for excitement and an unexpected result : it was a nailed on draw for four days ! Footman queries why play was allowed to continue in very poor light - I am in no doubt it was because Mr Bucknor was so p....d off at Pakistan's stalling tactics he wanted to give any English batsman fool enough to face up in the dark every chance of finishing the match. OK even admitting bias I thought it was excellent umpiring ...the spirit of the law rather than the letter. Ironically I think if Pakistan had not gone so defensive even after taking early English wickets then England would have either backed off the chase or taken the light at first opportunity...
And certainly the victory in India must also rate really high on the list ...for its manner and its recent rarity ! So a fair enough choice by BBC voters for top three.
Greatest win - in the strict sense of the word - though has to be Melbourne 2010/11. Not often you are sat in the MCG on the last day with a bunch of England fans and not an Australian supporter in sight