Clincher Wheels
Clincher wheels are the most common design seen among road cyclists. Clinch tires are left open on the rim side and are clamped or "clinched" into the wheel rim, sealing off the tube inside and providing a steady, easily-repaired ride. Clincher wheels are traditionally considered a low-performance training or budget setup, but with recent innovations in technology they can be made very race-worthy. These wheels also have the advantages of being low-maintenance, stable and generally burly.
Tubular Wheels
Tubular wheels are considered high-performance, high-budget race designs, although this stigma has lessened somewhat in recent years. Tubular tires completely surround the inner tube and are glued onto the wheel rim. Because of this, the overall wheel design can be made to be extremely lightweight; however, improperly glued tires can present safety hazards, and the wheels are generally difficult to repair and maintain.
Aero and Special Designs
Superlight, aerodynamic wheels are used during triathlon and time-trial races. Most of these designs incorporate an elongated rim design that either extends into or completely replaces the wheel spokes, reducing drag in that area and significantly improving aerodynamic performance. Time-trial specific wheels are also typically smaller in diameter than standard road wheels and use tubular tires--although larger, 700-centimeter rims can incorporate aero design features as well. Many standard road wheels have flat spoke profiles that provide some wind-reducing features while avoiding the expense and hassles of tubular designs.