Though there are dozens of chemicals that contribute to new-car smell, and that chemical cocktail varies by manufacturer, there are five common VOCs that make up most of the off-gassing found in the interiors of new cars:
Toluene: This liquid solvent comes from crude oil, though you probably know it best for its starring role in many nail polish removers. It's used in paints and glues, which can show up in a car's interior. It's also an anti-knock agent in gasoline, and it shows up in a car's exhaust.
Ethylbenzene: This is also a solvent, but it's a colorless, flammable gas. It's found in coal tar and petroleum, so it's probably not a surprise that it smells like gasoline. It's used in paint, but it's also used to create styrene (next on the list). Once it's off-gassed into the air, it breaks down into other (presumably less smelly) chemicals within three days.
Styrene: You won't find vast styrene deposits in nature — it's a synthetic chemical created in a lab (though there are small amounts of it in foods, including fruits and veggies). It's used in so many materials that will likely end up in your car, like rubber, insulation and carpet backing, that billions of pounds of the stuff are produced each year. It breaks down in the air within a day or two of being released in the off-gassing process.
Xylenes: This sweet-smelling, very flammable liquid is found in coal tar and petroleum. It's a solvent in both the rubber and leather industries, which is how it ends up in the new-car-smell mix. It's also one of the top 30 chemicals produced in the United States, so it's not surprising that it makes this top-five list of VOCs in your car.
Trimethylbenzene: This guy is an "aromatic hydrocarbon," though Toxipedia.org notes that it has a "strong, peculiar odor." It's a liquid used in solvents and thinners, as well as an additive in auto fuel. It breaks down in sunlight, so maybe parking in a sunny spot for a couple of days will help clear it out quicker.
If none of this seems appealing (and really, how could it?), just open your windows. Getting fresh air in the cabin of your car will clear out these VOCs more quickly and speed up the breakdown process for most of them.