Canada3 describes it well where the new car smell comes from and it is something like 80% toxins. However, it's diluted enough that it's not bad to our long-term health (as in we'll breath much worser stuff throughout our lives). However, certain people will be more affected by it than others and making one sick or want to puke are common symptoms. Also, the chemical makeup of the smell will be different with different manufacturing plants and even when a manufacturer changes supplier for an interior component.
As someone mentioned, the best ways to get rid of it quickly is to open windows as much as possible.
As an aside, I had the opportunity to visit my dealer yesterday and to sit in my Mazda3 for the first time (taking delivery Apr 1, but it has arrived to the dealership). My dealership is great in that it has in underground to store the new cars and at this moment mine is down there with it's windows open (I want to get rid of the new car smell too).