There are many different ways to classify card games, none of them entirely satisfactory. An excellent discussion of the difficulties can be found in David Parlett: A History of Card Games.
These abstract classifications are useful in understanding the evolution of card games and the relationships between them, but in a practical situation of deciding what card game to play, other types of classification might be more useful, and will be progressively added to this page in future. Some of these will be rather subjective. For example, in response to many requests, I have tried to produce a list of children's card games.