The low pressure at the center of this circulation causes the air over the top of the wing to speed up, and this sets up the whole pattern of the air going over the curved wing in the first place. The same effect can be observed when moving a spoon in a straight line through a teacup. Where there was once no circulation, two regions of circulation form in opposite directions. To understand this phenomenon better - try the Demonstration . Circulation at the start of the airflow over an airfoil.
Lift can occur on objects other than wings.
Lift is responsible for golf balls slicing into the woods and top spin lobs landing in the tennis court. To illustrate the slice, imagine the ball in the picture below traveling to the left while also spinning clockwise.