An intriguing and fun card game invented by David Parlett. Designed for three players, and outside of Skat, I think it's the best three-handed trick game out there.

Deck

Standard 52-card deck with all cards below 6 removed, plus one joker. If no joker is available, use the 2 of Clubs instead. Cards rank, high to low:
AKQJT9876

Deal

Deal the cards out in batches of 3. Turn up the last card to establish the trump suit. If the turn-up is the joker, the hand is played at no trump. Otherwise, the joker is treated exactly as if it were the turned-up card. This is to establish a random trump suit without forcing someone to disclose a card.

Bid

Each player now appraises their hand and decides how many tricks they will win. This must be an exact number; any more or less and you lose. Bids are not declared aloud. Instead (and this is the neat part), each player discards three cards that represent their bid.
Each diamond discarded represents 0 tricks
Each spade discarded represents 1 trick
Each heart discarded represents 2 tricks
Each club discarded represents 3 tricks
You formulate your bid by addition, so discarding 3 diamonds means you will try to win no tricks, discarding 1 club, one spade, and one diamond indicates 4 tricks (as would 2 hearts and 1 diamond, or 2 spades and one heart, etc). The rank of the bid-cards is irrelevant, only suit has meaning. The bid cards are placed face-down in front of each player and are not revealed until (possibly) the scoring.

Play

After all players have bid, left of dealer leads to the first trick. Players must follow suit if able, or else may trump or discard. Each trick is won by the highest card of the suit led or the highest trump if any are played. Remember, the object is to take exactly the number of tricks you bid. The winner of a trick leads to the next.

Scoring

After the 9th trick has been won, players count their won tricks and those who made their bids (took exactly the same number of tricks as they bid) turn their bid-cards face up and announce the fact. Scoring is as follows:

Each player scores the number of tricks he won, plus:
30 points if he was the only one successful
20 points if 2 players were successful
10 points if all 3 were successful
The game ends when someone reaches 99 or more points.

Notes

Skill at this game lies primarily in deciding the number of tricks to win and lose with the hand you are dealt. In this game, few hands are really "bad" because you can bid from zero to nine. The hardest hands are those that you could bid easily on but would have to discard crucial cards in order to actually bid that number.

Watch other players carefully during the play. A player who takes three tricks or so and then suddenly plays a low card to get rid of the lead has probably taken all the tricks they bid, and thus if you can force them to take another trick (which of course you intended to lose) they will not make their bid.

Note also that nine unknown cards (the bid-cards) are missing from play, so a Queen you thought you could get rid of by throwing it to the King or Ace may wind up winning instead if those cards have been discarded as bid-cards. Exploiting this principle, a fun thing to do if you cannot find a way to bid on a hand is to discard your three highest cards in the hope of confounding the other players when they turn out to be absent from play.