Navigation of a car-like robot in environments with unknowns requires effective on-line planning of nonholonomic trajectories. We propose a set of basic maneuver patterns based on Bezier curves that allow either forward or backward motion as building blocks to create nonholonomic trajectories quickly, given a sequence of knot positions/points (e.g., from some GPS navigator). These maneuver patterns are particularly useful for generating feasible trajectories in crowded environments with many narrow passages. We embed the above techniques in a new planner suitable for on-line planning of nonholonomic and collision-free trajectories, called the ON planner. Our ON planner enables that, given a sequence of rough knot points, a car-like robot can simultaneously plan and move in a geometrically unknown, crowded environment with local sensing towards a goal. Simulation results demonstrate the planner's nice capabilities.