Catch Games
Virtually any game involving catching or kicking balls or objects can be played in a backyard with three people. Examples include catching a football or frisbee, kicking a soccer ball and hackysack.
H.O.R.S.E.
The minimum number of players for a game of H.O.R.S.E., a modified version of basketball, is two, and can be played with virtually any number of people beyond that. All that is needed is a basketball, a flat surface on which to bounce the ball and a hoop.
Four Square
Though Four Square is traditionally played with four players (hence the name), you can amend the game to three players. Essentially, the rules remain the same for the most part: bounce the ball from square to square until each player who makes an error is eliminated. All the materials needed are a bouncy ball (basketballs can be used, though tend to be harder on the hands in this scenario) and a flat surface in which it is possible to connote boundaries between squares. This can be done simply with chalk.
Backyard Bowling
Backyard bowling is easy to set up and versatile for any-sized group, as this game has the option for teams or individual players. If you don't have bowling pins, any household objects will do: empty soda cans, cereal boxes or even stuffed animals. Any ball will do, especially if the objects you use as pins are fairly easy to knock over.