Boat controls have been broken since the snapshots after 1.5.1. You can only move forward in a boat with your keyboard. You can not move left or right or even push down to make the boat stop. You can only steer with the mouse and have to wait for the boat to come to a stop on it's own.
Duplicate of MC-14521, please use the search function to see if your bug has already been submitted. Currently over 56% of tickets are being closed as duplicate.