What strange chess rules can you think up?

You should be able to capture your own pieces.

Play with a standard deck of cards as well.

After each turn you may draw a card.

Instead of moving a piece you may draw a card. (This is in addition to the card drawn at the end of the turn.)

Instead of moving a piece you may play five cards from your hand, forming a poker hand. The effect of this depends on the hand you've played:

One pair: Add a pawn to the board.

Two pair: Add two pawns to the board.

Three of a kind: Add either a knight or the bishop to the board.

Straight: Add a rook to the board.

Flush: Add a rook to the board.

Full house: Add 20% of the starting time to your clock, and then make a move. (E.g.: in 1 minute bullet, add 12 seconds; in 5 minute blitz add 1 minute; in 45 minute classical add 9 minutes, etc...)

Straight flush: Add a rook and either a knight or a bishop to the board.

Royal flush: Add a queen to the board.

sounds very fun!

but unfourtunatly I don't know many poker hands.   :(        

Mission cards, a la Risk, which would reward a player for completing some task. For example: Bring a knight to a corner square and you get to move twice in a row.

I like the way you think. I have made a chess variant where you start the game normally and then each player may once during the game roll a die to activate a chess variant (I have a variant for each number written down). One of the variants is that a knight in the corner is allowed to move 3 times during the same turn (with the turn ending if it becomes a check). That variant has never been activated when I have played with my friends though, but I think it is one of the interesting ones to add a new dynamic to the game.

I have also been thinking about making a new chess variant (not included in the above) that involves cards, but it is just ideas at the moment).

Sounds fun, although I am not a big fan of adding time to your clock since usually the board is more important than the clock as long as you manage your time well.

I want to mention the economy chess variant which you might be interested in. It is a variant where you get income based on the numbers of squares you control and you can spend coins for new pieces during the game. A bit different from your variant when you draw cards and spend poker hands to get pieces, but I thought you might be interested since the ideas of getting more material is somewhat similar. More detailed rules can be read in the forum in the group.

http://www.chess.com/groups/home/economy-chess

http://www.chess.com/groups/forumview/standard-rules-of-economy-chess

I made some modifications and called it Poker chess. I might want to modify some rules in the future, but here is my first set of rules for it.

Poker chess:

Poker chess is played with a standard deck with 52 cards. After each move the player that moved draw a card. If that player have more than 5 cards, then that player discards a card. During a players turn, before he makes a move, a player may show his hand and add material to keep in reserve according to the list below. Then that player discards his hand. The pieces in reserve can be played as in bughouse chess, with addition that a king can get placed this way too (and the king can be placed regardless whether a player is in check or not). If a player has 2 or more kings, all except one needs to get captured before the other player can do any check/checkmate.

1 pair = 1 pawn

2 pair = 2 pawns

3 of a kind = knight/bishop

Straight/Flush = rook

Full house = knight/bishop + pawn

4 of a kind = knight/bishop + knight/bishop

Straight flush = queen

Royal straight flush = king + queen

Every five moves a pawn gets teleported randomly to another square on the board between rows 2 and 7, as determined by a RNG.

The king can take protected pieces but not be taken.

The queen cannot be taken under any circumstance.

roll the dice to move a piece

Care to explain how that would work?

I move pieces by lifting them with one hand and release them on the square I want to move to. Should I roll the die so it touches the piece and with enough force to make the piece move to the square I want instead? 

Phone chess, call in your moves.  

Pieces as well as pawns may capture en passant.

Kings can move multiple spaces on Tuesdays.

 quick chess: after 20 moves, whoever has more material wins. pawn is 1, knight is 3, bishop is 4, rook is 5, queen is 9, king is 0

but what about the knight?  

-Maximus wrote-