In open-wheel racing, such as Formula 1, Indy Racing League, Champ Car and Top-Fuel Dragsters, wings are used to hold the car to the racetrack. This is called aerodynamic grip. The principle is exactly the opposite of an airplane; airflow over the wings on the nose and tail of the car forces it down onto the track at high speed, rather than allow it to take flight. This is what makes open-wheel cars so incredibly fast and maneuverable, even on flat (non-banked) turns.
In stock car racing, the body of the car is shaped to allow for the best possible aerodynamic grip. In the old days, cars looked identical to their showroom counterparts (essentially they were modified for racing), hence the name "stock" car. During the heyday of Richard Petty, David Pearson, and Benny Parsons (1960's and '70s), the cars were big and boxy. Engine horsepower was used to make the car go fast. Eventually teams learned that air flowing around the car was a problem, especially when cars were closing on the 200 mile-per-hour barrier. Strips were added under the front end of the car, and another on top of the rear decklid. These strips were called spoilers, and acted to spoil the airflow under the car, and cause turbulence over the rear. This improved control by keeping the nose down and pushing the rear of the car onto the drive wheels - rear downforce. Speeds further increased as a result of these innovations.
The 1980's saw NASCAR go through a transition in which races cars became "aero coupes" more than "stock cars." Corners were rounded off, windows sloped more to reduce drag, and large valences (front and rear bumper fairings that improve aerodynamics, and side fairings to prevent airflow under the car, possibly creating dangerous lift) were added to run the nose down so it was almost touching the racetrack. The less air under the car, the more stable it is. The smoother that air flows over the car, the faster it is and better it handles. The cars still resemble their showroom counterparts in basic template, which must be strictly adhered to by the teams, but headlights are gone - replaced by decals creating the appearance of them, and the shapes are more refined for speed.
Depending on the type of track being raced on, different front end valences are used by the teams. All have grille openings to allow air to flow into the radiator and cool the engine. These appear rather similar to cars on the road. For short tracks and road courses, you'll see additional intakes for the brake ducts. These help keep the enormous drilled disc brakes cool, improving their performance (heat causes brake "fade," reducing effectiveness and forcing the driver to run slower to compensate). For speedways and super-speedways, tracks where speeds are consistently high and brakes are used more to trim speed going into turns, the vents and ductwork are removed. Speed is the key - any opening on the front of the car creates drag, and drag is bad.
Enter the household item: duct tape, a.k.a 200-mph tape. Tape is used as an aerodynamic tool in NASCAR, as well as a repair device. If you look at pictures of the cars, you'll see the grille openings on the front. Teams will cover these with tape to improve aerodynamics and increase speed. If you watch qualifying, you'll see the openings are completely covered. The cars will only make 2-3 laps around the track during a qualifying run. The engine runs more efficiently when it is warmed up. Closing off the airflow to the radiator allows the water temperature to rise quicker. Once the car completes its run, the engine is shut off to prevent overheating. Occasionally you'll see steam venting from the right side base of the windshield. This venting is acceptable for the short period a qualifying run takes. Completely covering the openings allows for maximum performance, aerodynamics, and speed during qualifying.
For racing, you'll see a small opening in the grille, while the remainder is taped over. This tape is usually color-keyed to match the car, but it's visible in front-end shots. The tape runs horizontally over the opening, and is laid on in strips. The size of the opening is kept to an absolute minimum - large enough to allow sufficient airflow to the radiator to keep water temperature at about 220 degrees Fahrenheit. Should the temperature rise the pit crew can remove tape to allow more airflow into the engine. Usually the first row of tape above the opening is split into two or three small sections, and each piece will have an end folded under to make a tab. This tab can be quickly grabbed and pulled off by a crew member during a pit stop. A few square inches of exposed grille can make the difference in controlling water temperature.
The second use for duct tape is to adjust the car's handling. This may sound bizarre, but it works very effectively. During the race, adding or removing a piece of tape is the only option the crew has to adjust the aerodynamic grip of the car. As air flows over the nose of the car, it presses it down onto the track. This results in the steering wheel better gripping and turning the car properly - forward bite. Air flowing into the grille, though essential in cooling the engine, creates drag and slows the car. The opening is usually centered to create balance in the handling of the car. During practice or a race, the team may add (or remove) vertical strips of tape at the edges of the opening. Though small, these strips can change the handling of the car by creating more downforce on that side of the nose, allowing the car to make better (read: faster) turns.
The third use is the least common, but sometimes the biggest difference-maker. Should the car be damaged in a collision, the crew has several options to repair the damage. In recent years, teams have brought pre-shaped pieces of fiberglass or sheet metal that can be pop-riveted into place to restore aerodynamic flow. The edges are then usually covered with tape to reduce drag. Tape can and is used to hold parts on, but tends to not last long under stress - thus the pop-rivets for mechanical attachment. Small crinkles in the hood, bumper, or fender are more often covered with a patchwork of tape.
So next time you see different colors of duct tape at your local hardware store or home improvement warehouse, thank NASCAR. After all, plain grey just doesn't go well with some of those bright paint schemes. In a sport that's all about speed, aerodynamics aren't just a tale of the tape.