I've recently been looking at several other revolutions, such as the French and Russian revolution, and while they were initially successful, as in the power of the previous ruler was removed, both really just eventually put another dictator into power, going against the purpose of the rebellion. This isn't really the case with the American Revolution, since the colonists were able to create a stable form of government which mostly aligned with their beliefs during the revolution. Why is this?
Note, I mean ideologically, not militarily. And didn't notice the typo in the title, sorry.
The American Revolution differs from the other revolutions you mentioned in an important way - it didn't have to alter the society in question as much. During both the French and Russian revolutions, not only were the entire governments rebuilt, but the structure of society and the economy torn apart, reimagined, fundamentally challenged in serious ways. The American Revolution, by contrast, left the American ruling elite in place and left the structure of the American economy largely untouched. The British military had to be contended with, certainly, and the government rebuilt, but these actions were carried out by men who had already been elites and had experience from the old system. In a way, the nomenclature is misleading - those participating in the American Revolution faced an entirely different set of challenges than those participating in the Russian Revolution or the French Revolution. A revolution overthrowing the power structure in one's own country is really a distinct undertaking from a revolution removing the influence of another, external force.
I think a lot of people, Americans in particular, overstate or overestimate the degree of radical change the American Revolution embodied. At the end of the day, the fundamental social, economic, religious and even political constructs of British society remained fairly intact, whereas the French and Russian revolutions were essentially attempts to build entirely new countries on the ashes of the previous regime.
Also worth noting is that the Revolutionary War itself was fairly minor, in terms of casualties, economic damage, and social impact; believe it or not, only about 6,000 Americans and 4,000 British soldiers died in combat, though disease, starvation and exposure lead to about 25,000 additional casualties on the American side. Civilian populations were left basically intact, cities weren't intentionally razed to the ground, and there was no coordinated attempt to purge the political or economic elite; compared to other wars of independence or revolutions in that time period, like the Haitian Revolution, the whole thing was relatively contained and polite*.
Honestly, even the Constitution didn't represent a mind-blowing change for most British-soon-to-be-American people. The Parliamentary system in mid-eighteenth-century Britain had already devolved huge amounts of power from the monarchy to Parliament (a process that picked up speed after the Treaty of Union 1706) and while the King of England certainly had plenty of authority (and George III in particular attempted, without success, to reverse the process of royal marginalization), he wasn't an absolute ruler by a long shot. In other words, democracy wasn't a new or foreign concept; the Constitution just took it further than the British had. Even the Bill of Rights, which contained a number of pretty radical ideas, was largely codifying or expanding rights found in British common law.
I don't mean to give the impression nothing new or innovative came out of the Constitutional convention, or was found in the new nation- that's not the case at all. It's just that the degree to which society changed is typically overestimated.
*In case it's not obvious, I'm being partially facetious here- but there's a grain of truth to it. The response to other contemporary revolutions was far more brutal.