Road bikes incorporate an array of technologies to improve performance, but one of the most fundamental on any road bike is the wheels. There are many companies engaged in the manufacture and marketing of bicycle wheels, since it's one of the simplest and most effective upgrades a cyclist can do to their bike--good wheels can improve the performance of any bicycle.
When considering wheels for your road bike, it's important to understand some distinctions among the varying types available on the market.
All-purpose wheels are best distinguished by their traditional profile and spoke patterns, featuring narrow rims. These wheels can be used for any purpose from recreational riding to training to racing. Since these wheels do not feature the deeper rim cross section of aero wheels, they're often lighter and chosen by riders who want a light wheel for climbing or one that lets them accelerate quickly in racing situations.
Aero wheels are becoming increasingly common, especially among riders who participate in triathlon and time trial racing, where the emphasis isn't on racing tactics but racing solo against the clock. The deep rims of aero wheels provide less air resistance, so the rider can maintain high speeds with less effort. The depth of the rim can vary greatly on aero wheels, including the extreme of a full disc wheels for the back wheel of the bike.
Aero wheels have the disadvantage of increased susceptibility to cross winds, which can make handling difficult. They can also be a bit heavier than all-purpose wheels. Nonetheless, even some all-purpose wheels are starting to incorporate aero elements, like slightly deeper rims.
Clincher vs. Tubular Wheels
One important distinction in road bike wheels is the method of affixing the tire to the wheel.
Clincher wheels are the most common. In a clincher wheel, the tire is held onto the rim of the wheel with wire beads that run around the inside perimeter of the tire--they clamp onto the rim of the wheel to hold the tire in place. The air in a clincher tire is held in a tube inserted in the tire. Clincher wheels are used on the vast majority of tires built for recreational cyclists -- they offer excellent performance and make it easy to change tires or repair a flat.
Tubular tires are glued onto the rim of the wheel, and have no tube -- the air is held within the tire. Tubular tires traditionally have been used for high-end racing bikes. Some cyclists say they prefer the "feel' of a tubular tire. Mounting a tire to a tubular wheel involves gluing the tire onto the wheel and requires a bit of expertise to do the job well.