What do the American, French, and Haitian Revolutions have in common? Differences?

Each of these revolutions was very complex, so any brief answer will be very incomplete. That said, there are several points of comparison and contrast that we can look at. We should also bear in mind that these revolutions were interrelated. France's expenditures on the American Revolution helped create the crisis that led to the French Revolution, and the Haitian Revolution occurred directly as a result of the turmoil in France, of which Saint-Domingue was a colony. 

One major point of comparison would be that each revolution was influenced to some extent by Enlightenment ideals. We see this in the American Declaration of Independence and the French Declaration of the Rights of Man and of the Citizen, both of which express Enlightenment ideas about fundamental human rights. But the Haitian revolutionary leaders were also influenced by Enlightenment thought. Toussaint L'Ouverture, in particular, was deeply read in the French Enlightenment. Each revolution had liberty as its central goal, with both the Americans and the Haitian Revolutionaries struggling for independence from the mother country. Each revolution also involved a staggering amount of violence in a protracted war. 

A major difference was that the Haitian Revolutionaries (eventually) sought freedom for slaves. This was a major reason why the United States under Thomas Jefferson refused to give recognition to Haiti, and in fact the French under Napoleon attempted to crush the Haitian Revolution for this reason. Some historians have argued that the American Revolution featured less internal disagreement and strife than the French and Haitian Revolutions, but others tend to disagree, citing many places (like the South) where the Revolution was basically a civil war between Whigs and Loyalists.