In medium saucepan, bring water, sugar and ginger to boiling over medium-high heat; reduce heat. Simmer, uncovered, for 3 to 5 minutes or until the mixture thickens slightly. Remove from heat; let cool to room temperature. Strain mixture through fine mesh sieve, discarding solids. Cover and chill for 24 hours or up to 2 weeks.
Just before serving, pour 1/4 cup ginger syrup into ice-filled tall glasses. Slowly add 1/2 cup club soda to each glass. Stir gently to mix. Garnish each glass with a lime wedge. Makes 8 (6-ounce) servings.