Best definition of Game: A problem-solving activity, approached with a playful attitude. Alternative: A rule-based formal system with a variable and quantifiable outcome.
Book: The Art of Game Design
Although there's no perfect definition of games (or perfect definition of anything; see Language Games and Family Resemblance), good definitions have value if they give you some insight into making better games. There are several different attempts to define what a game is.
Sid Meier, the game designer behind the Civilization series, has a simple definition:
"A game is a series of interesting choices".
Ernest Adams and Andrew Rollings's in Andrew Rollings and Ernest Adams on Game Design:
"One or more causally linked series of challenges in a simulated environment."
These two definitions remind me of Steve Jobs's "taste is a byproduct of the number of decisions you make", but a bit too abstract to be useful.
Katie Salen and Eric Zimmerman define game in their Rules of Play: Game Design Fundamentals:
"A game is a system in which players engage in an artificial conflict, defined by rules, that results in a quantifiable outcome."
And Jesper Juul in his book Half-Real: Video Games between Real Rules and Fictional Worlds defines game as
"A rule-based formal system with a variable and quantifiable outcome, where different outcomes are assigned different values, the player exerts effort in order to influence the outcome, the player feels attached to the outcome, and the consequences of the activity are optional and negotiable"
But my favorite one is from Jesse Schell in The Art of Game Design:
"A game is a problem solving activity, approached with a playful attitude"
I like this definition because it provides more philosophical depth compared to Jesper Juul's definition, which feels more prescriptive. It captures the essence of the game while allowing game designers the flexibility to establish their own rules
Jesse Schell also defines a Good Toy as "an object that is fun to play with ", Fun as "pleasure with surprises", and Play as "manipulation that indulges curiosity".