Most of the road bike wheels you see use clincher rims. Clinchers use inner tubes, which makes them easier to service in the event of a flat. Clincher tires are also less expensive than tubular tires, and thus more suitable for training and recreational racing. Clincher rims' drawbacks are heavier weight and greater rolling resistance than tubular rims.
Tubular rims are less common than clincher rims, and they are generally used for racing. Tubular rims provide less rolling resistance than clincher rims. They are tubeless which makes them lighter, as well. Changing flats can also be difficult with tubular rims, since they are glued in place.