I was thinking about this a few days ago. This may or may not be right, but it makes sense to me.
If you ignite the gasoline, let's assume that on an energy diagram, you've reached the activation energy. So, the bonds in the gasoline break. Also, let's assume that gasoline is made of a single type of molecule, for simplicity.
Now, the atoms in the gasoline are in an excited, high energy state, but as is the nature of the universe, things want to go to a low energy state. Before, the atoms were bonded in gasoline, which can be considered a relatively low energy state.
The atoms now have a few possible results. They can go towards the formation of a chemical product that will put them into a low energy state, with the lowest energy state possible is the most favorable. If, with the atoms avaliable in the surrounding area, gasoline is the most favorable energy state to be in, then they'll reform gasoline and there won't be a chemical reaction.
However, with oxygen at hand, the hydrogens and carbons may form the products of CO2 and H2O, which presumably will put the atoms into a lower energy state than gasoline. However, putting atoms into a lower energy state means that the energy has to go somewhere. That energy is expelled from the atoms, which generates heat, and, I guess, flames/combustion/and all that goodness.
If anyone can correct this, feel free to. I'm a biology major, not a chemistry major, but I'd like to know the answer to something like this :]