Combine first 4 ingredients in a medium saucepan; bring to a boil. Add flour, all at once, stirring vigorously over medium-high heat until mixture leaves sides of pan and forms a smooth ball. Remove from heat.
Stir in vanilla. Add eggs, one at a time, beating with a wooden spoon after each addition until smooth.
Pour oil to depth of 2 inches in a large Dutch oven or heavy saucepan; heat to 370°. Spoon batter into a large decorating bag fitted with a large star tip. Pipe batter in 6-inch strips into hot oil, in batches, and fry 3 minutes or until golden, turning once. Lift out with a wire spatula, and drain on paper towels.
Combine sugar and cinnamon in a shallow dish. Roll churros in sugar mixture. Repeat with remaining batter. Serve immediately.