Rummy is a generic term for card games of the same family as gin rummy. One can speak of the rummy family of games; to refer to rummy is probably to mean gin rummy, but strictly there is no one rummy game. It is perhaps more satisfactory to describe these as matching card games. The family extends to include Canasta, for example. David Parlett (The Penguin Book of Card Games, 1978) describes the Mexican game of Conquian as being ancestral to all rummy games.

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Billabong Boardgamers - Mystery Rummy Jack The Ripper review.
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Billabong Boardgamers - Review of Mystery Rummy Rue Morgue.
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Bruno Faidutti - Review in English and French of this serie.
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Game Night - Review of Jack the Ripper.
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Game Night - Review of Jekyll and Hyde.
Spotlight on Games - Rules at Rick Heli's site.
The Game Report Online - Review by Nick Sauer of the two first games in the serie.