You can argue Fonteyn & Nureyev (and their Romeo & Juliet was something to see), or Nijinsky & Karsavina, or Gene Kelly and Jerry the Mouse, but for my money, it was and always will be Astaire & Rogers, as this tribute demonstrates.
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I saw Fonteyn and Nureyev several times, and they had that spark too. Obviously also the amazing talent/ability. But Astaire-Rogers had the genius je ne sais quoi. You can’t train or rehearse for that. And they did it in very few takes, I have heard. Had to polish those floors in between takes, too.
They were stellar dancers and had that special connection on the screen, that certain charisma and spark. Loved them. Still do.