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How about Snidemost Chess: after each move, the opposing player must
immediately make a sarcastic and cutting remark. For example:

1. e4

Black: 'Oooh! Hold on to your hats! Haven't seen that one before! What oh
what shall I do now?'

Ralph has provided an interesting theme which can be developed in different
ways. Colorboundmost Chess emphasizes the race to mate theme too strongly
for my taste.  Nearly Colorboundmost Chess would be more playable.  

I have any idea for a game which emphasizes colorboundness but not to the
degree of either of these variants (based on Peter Aronson's An Odd Piece
comment).

King and pawns are standard FIDE.  The Rooks move as Dabbabah-riders and
capture as Rooks (mDDcR).  The Bishops move as Alfil-riders and capture as
Bishops (mAAcB). The Queen combines the Rook and Bishop (mAADDcQ).  The
Knight moves as Narrow Knight and captures as Knight (mvNcN).

The pieces move to half of their normal squares but capture normally.
Rooks, Knights, and Queens are initially confined to 1/4 of the board and
the Bishops to 1/8 of the board, but by capturing, each piece has its
normal reach.

Except for the moves of the pieces, normal FIDE rules would apply and the
colorbound castling rule in Rule Zero would apply.

Snidemost Chess was played by the ancient (and weak) computer chess game
named 'Boris'. 

Most of the other suggestions have already been implemented under
different names, I think; however, however....

Castlingmost Chess: all moves must castle. Any piece can castle with any
other piece, friend or foe; and of course a piece can participate in
castling more than once. Owner chooses promotion. Example: 1. a2-d5 (and
f7-c4), a8-a5 and a2-a6 2. a6-b7 and b7-a6; advantage W because the Pawn
ptomotes. (You may not make a move that merely is an undo of the
opponent's move.) The game is won by mate and there are no captures and no
stalemate.

Not play tested much. It may need another rule or two.

========

I've been on vacation.

Oops, your example starts off with a diagonal castle.  Duh!  Sorry, please
disregard my first question.

Yes, diagonal 'castling' is permitted -- and necessary to the game.

If an even number of squares, each piece crosses the midline: a2-d5+f7-c4;
a1-a5+a8-a4; a3-a5+a6-a4; a4-a5+a5-a4.

If an odd number of pieces, the piece initiating the castling occupies the
midpoint: e1-c1+a1-d1; e1-d1+c1-d1; and so on.

Just like FIDE Chess.

I have been waiting for somebody to notice that, in Castlingmost Chess,
once you vacate a corner square that square can never again be occupied;
and if a8 is empty and you vacate b8, b8 must forever stay empty; and so
on.

Because there are no captures, this has interesting implications!!

One more question on Castlingmost Chess:
If there are no captures, what does a 'mate' look like?

> If there are no captures, what does a 'mate' look like?

It's what we call 'pictorial' mate. That is, if you look at the diagram it
appears to be checkmate, even though the rules of the game do not permit
capture. 

In other words, when it comes to check, the pieces have their normal
powers. It's a funny situation, and although I cannot think of an example
right now, I know that there are several variants that use this concept.

For an example, what's the fastest foolsmate?

1 Ke1-e2+e2-e1, e7-e4+Ke2-e5 is a promising start, but now what? Kf6+g7-e5
is illegal -- cannot put self in check -- and K can retreat from check by
Castling with b2 or h2. I said you can castle out of check, right? Maybe
that was a wrong choice.  

The foolsmate is not easy to find.

I liked this game.  And also i liked Pitt Bill's ideas (if games, he suggested, already exists, please, give links here); I have also some ideas:
game, where all non-capturing moves are different from capturing;
game, where all pieces must leap to move (like cannons in Korean chess);
game, where all turns are promotion;
game, where all pieces must (or, at least, can) use both orthgonal and diagonal moves in same turn (like gryphon);
game, where all pieces always can go almost anywhere (with different restrictions);
game, where all pieces are compound (the last is probabbly stupid idea)...

Good idea. But rules of this game are easier to understand and remember:
/play/erf/Colorbou.html