It's not just the Olympics, they compete as Great Britain in most international team events. For the Six Nations, it was originally the Home Championship for the four countries of Great Britain and Ireland, before they admitted France and Italy.
Cricket is seen as almost exclusively English (Scotland of course competed at the last World Cup), football is down to the Home Nations (inventors of football) having four votes at the FIFA Congress. Most of the associations refuse to join together, partly fearing they'll lose their votes, and partly fearing they won't have any players good enough for a unified team.
And as for the Commonwealth Games, I guess it's more of a privilege for the former owners of the Empire to field as many teams as they can (as well as England, Scotland, Wales and Northern Ireland, the Isle of Man, Jersey, Guernsey and Sark also compete).
(As to the Olympics, it's officially Great Britain and Northern Ireland, as Great Britain is the main island holding England, Scotland and Wales.)
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