In this large group of draw and discard games, the object is generally to improve one's hand by forming it into sets of matching cards (usually groups of the same rank or sequences in a suit). The basic move is to draw one (or more) cards from an undealt stock or from the (face up) discard pile, possibly meld a set or sets, putting them face up on the table, and then discard a card.
Rummy games seem to be ultimately of Chinese origin. Although they are now widepread throughout the world, games of this sort were unknown outside the orient until the twentieth century. David Parlett's History of Gin Rummy, originally published on the Game Account site, also includes some material on the history of Rummy games in general.
Here the aim is simply to form your whole hand into sets as soon as possible. When someone succeeds in this and goes out, the other players may lose a fixed amount, or may be penalised according to the number of unmelded cards they have left.
In this group of games, which are ancestral to all western rummy games, the objective, as in western rummy, is to complete a hand consisting entirely of valid combinations. However, the draw and discard mechanism is somewhat different. Cards drawn from the stock or taken from the discard pile are never added to a player's hand. A player can take the last discard only by immediately using it in a meld, which is exposed on the table. The alternative is to turn over the next card from the stock and place it on top of the discard pile to be used in the same way.
Like Western basic Rummy games these are draw and discard games in which the aim is to go out by forming your whole hand into sets. The Asian games are played with a variety of different types of cards and tiles, and the nature of the sets needed to form a complete hand varies from game to game. In some cases it is possible to claim a player's discard out of turn if you need it to complete a set. In some games, some sets or hands are more valuable than others, so that the amount won by the player that goes out depends on the quality of the winning hand.
The object is the same as in Basic Rummy, but in each deal, each player's first meld has to conform to a pre-determined contract. Generally, the contract becomes more difficult through a series of deals.
Again the aim is to get rid of all your cards by melding them. The distinctive feature of these games is that when melding, you are also allowed to rearrange the existing melds on the table to form new melds incorporating cards you add from your hand.
In these games, you do not necessarily have to form all your cards into sets to go out. You go out when you think that the value of your unmatched cards (deadwood) is less than that of the other players. If you are right you win, but if another player can do better you are penalised. Examples of this type are Gin Rummy and Tonk.
In this type of game positive points are scored for melds. There is still an advantage in going out, but it is also necessary to consider gaining points by making valuable melds. 500 Rum and Mah Jong are games of this type.
This is a particular type of Meld Scoring Rummy with special bonuses for melds of seven cards, known as Canastas.
At Game Duell you can play Rommé (German) or Rami (French) online for fun or real money: they offer a variant using two decks and 6 jokers, in which a player's first meld must be worth at least 40 points.
Special K Software has software to play many of the games in the Rummy family. This includes Gin Rummy, 500 Rummy, Oklahoma Rummy, Michigan Rummy, Boat House Rummy, Pinochle Rummy, Kaluki, Round the Corner Rummy, One Meld Rummy, Wild Card Rummy and Indian Rummy. This software is available at www.specialksoftware.com.
Randy Rasa's Rummy-Games.com has reviews of many rummy software packages and on-line servers, as well as rules for various rummy games.
The German site Skill 7 includes online versions of Gin Rummy, Canasta, Rummy (a 13-card game with a minimum 30-point requirement to meld) and Jolly (a meld scoring rummy game with jokers).
Links to other software for particular types of Rummy will be found on the relevant pages.