Disregarding negative externalities and other barriers, what are some fuels that have a higher power density than gasoline?
I would suggest you take a look at what they use as rocket fuel.  There are a lot of fuels with higher power densities but they wouldn't work well on the highway. 

The Navy has had great success with powering vessels on nuclear energy.  That is the ultimate top of the viable fuel density list.  Maybe one day fusion will become viable, then it will be at the top of the list.  

As for the second part of your question, the characteristics of chemical fuels have to with free radicals.  

Any viable fuel needs to be readily split into component parts (triggered by a spark or sudden compression or the like) that then combine in other configurations in an exothermic reaction so you get a net energy output.