New Variant

There are a great many variants that are possible.

Equal Women's Rights chess:

The queen is reduced in mobility to the same as a king. No more of that wonder woman crap... Castling rules apply to the queen the same as if it were a king. Mating either king or queen is a win.

Affirmative action chess:

White starts out normal. White plays normal chess. White has first move. Black has no army at all on the board. Black has a full crazy house army in the pocket. Each piece and pawn may be dropped 1 time for black. (8 pawn drops 1 queen drop 2 knight drops 2 bishop drops 2 rook drops)

Pawn Grubber Chess:

The same as normal chess in terms of piece setup and movement, and rules. The only difference is the king is no longer important. Checkmate is not a thing. Winning all 8 enemy pawns is the only way to win.

How about breading chess? If Piece A is the same color and type of Piece as Piece B and the only reason that Piece A cannot move to the square that Piece B is on is because it is occupied by piece B then a new piece can be placed on a square that Piece B could move to while Piece B remains on the same square it was on. If piece B is absolute pinned to the king the new piece can still be placed on a square that Piece B would be able move to if Piece B was not pinned. A new pawn can be placed using the same rule as for pieces but cannot be placed on the 1st rank or 8th rank. Also if a queen is next to the king of the same color then a new queen can be placed on one of the squares that the parent queen could have moved to while the parent queen remains on the same square that it was. All the rules with the exception of those I just mentioned would be the same as normal chess.

What @FalconPower is suggesting is called "The Grand Crossing," see more here: http://www.chessvariants.com/winning.dir/grandcrossing.html

that's literally called Racing Kings...