When does white do it? Why does white do it? What kind of strategies should both sides adopt in such games? What kinds of games does it give rise to (i.e. positional or tactical)? Which players are well known practitioners of such a setup as white?
The most common way to end up with queenside castling for white in the KID is via the Saemisch Variation
The link above notes that
True enough, and so did Alekhine. But if my database is to be trusted, none of these champions has all that many games on record in the Saemisch, and even less against serious competition. For instance, Karpov played such a setup twice in his 1990 world championship match against Kasparov, scoring a draw (round 21) and a win (round 23), which is a nice endorsement. But he seems not to have played that way often; in my database, the only other classical game for Karpov in this setup against a player who is truly a peer of his is a draw against Timman from round 18 of their 1993 FIDE championship match.
The late Svetozar Gligoric has 18 games on the white side of this in my database (scoring 12.5 points), and his games could be particularly enlightening since he was a well-known proponent of the black side of the King's Indian; in fact, I also see him scoring 22.5/37 on the black side of this, so there's plenty of Gligoric games from boths sides to chew on.
But the most frequent assayer that I find is Florin Gheorghiu, and he's also a very successful one, with a phenomenal 35.5/43 score. So if you want a "hero" to follow for this kind of setup, Gheorghiu might fit the bill nicely. (Or conversely, if you want to know what might be coming at you as black.) To whet your appetite, what follow are two of his wins, each with Gligoric playing black in fact. The first is from the 1966 Havana Olympiad:
And the other is from the 1968 Lugano Olympiad: