Thanks for being patient through my move. We're all settled in the new house (except for the piles of boxes still in one corner of the living room.) If you don't know what I'm talking about, please follow me on twitter for random life stuff.
Chess, whist, checkers, quadrille, backgammon, piquet, quinze, Vingt-Un (AKA blackjack), pharo, rogue et noir, cribbage, matrimony, cassino, reversis, put, connexions, all fours, and speculation are just a small sampling of games played during the late Georgian and early Regency eras.
Many card, dice, and board games played during these years are played in modern day, so I'm going to focus on a few games that are more obscure in modern game play and are sometimes seen in romance novels. These will be quick overviews, so if you would like more info, I recommended google books where you can find period books with long descriptions of rules and etiquette.
Whist - the polite parlor game
Whist is played with four players, but may be played with three and a dummy hand. Each has a thirteen card hand.
This is a suited card game with trump. If you've played hearts, spades, euchre, or any other suited card game, you know that you play by following suit. (For example, your opponent leads a spade, you must play a spade, if you have one.) If not, you may play any other card, including trump cards. Trump suit--determined by the card the dealer turns face up on the table--beats all the other suits. (For example, if hearts are trump, a 2 of hearts beats an A of clubs. However, an A of hearts beats the two of hearts.)
To win a point, you and your partner must take 7 hands. If you do, you get a point. If you received ten points during the course of play, you win.
Pharo (or Faro or Pharaoh) - the coffee house game
This is an odd cross between high/low and roulette. The dealer lays out a winning and a losing card, and the player bets on which card might win by placing a chip on the number or face of the card. You can also place bets on groups of two, three, or four cards by placing your chip between cards. If you have a chip placed on a winning card, and it is the winning card, you win. If you have a chip placed on the losing card and it loses, you lose.
Hazard - the dice game
This is somewhat complicated, so I'll just say it's similar to craps and give a general idea of how it's played.
The betters choose a number between 5 and 9. The roller rolls two dice. The betters win if the roller rolls the same number twice before rolling a losing number. A 2 or a 3 (and possibly 11 or 12 depending on the number you choose) are losing numbers. Alternately, 11 or 12 might be winning numbers depending on the number chosen.
I hope you enjoyed reading some general descriptions of the games you might read about in romance novels. These certainly aren't the only ones, but they are the more popular ones.