A common house rule for the base game is that when a pawn gets promoted to Queen, that Queen can be represented with an upside down rook. This can happen when the actual Queen is still on the board and no replacement is available. This house rule is actually included in the official United States Chess Federation rulebook, but not in the FIDE rules that are used in the rest of the world, and doing so under those rules will result in an arbiter coming to the table, turning the Rook back the right way up and forcing you to play on with the "Queen" becoming a Rook instead.
Classical time controls (at least 2 hours per player) may be the "default", but there are also faster time controls like rapid (15 minutes plus 10 seconds additional time per move), blitz (3 minutes plus 2 additional seconds per move) and even bullet (less than 3 minutes total per player). Rapid and blitz have their own FIDE-sanctioned tournaments.
Fischer Random Chess, also known as Chess960, is a variant that randomizes the opening setup in order to downplay the memorization of openings and force players to evaluate the game over the board. It's popular enough that it was acknowledged by FIDE in 2008 and got its first sanctioned tournament in 2019, with many top chess players attending.
Urban Legend of Zelda: "Vertical Castling" supposedly took advantage of a loophole in the castling rules that allowed you to castle using your King and a newly-promoted Rook (which was technically unmoved), causing FIDE to add an Obvious Rule Patch after its discovery. In reality, even the original FIDE laws from 1930 prohibited this by requiring that the king and the rook must be on the same rank.
, also known as Chess960, is a variant that randomizes the opening setup in order to downplay the memorization of openings and force players to evaluate the game over the board. It's popular enough that it was acknowledged by FIDE in 2008 and got its first sanctioned tournament in 2019, with many top chess players attending.