Separation of Powers in the States
Often quite different from the federal system.
The post about the Kentucky AG suing the Kentucky Governor post is a good reminder that the separation of powers operates very differently in many states than in the federal government. At the federal level, the executive power is vested in the President (though there are some disputes at the edges about independent agencies); but many states have independently elected executive officers—Governors, Attorneys General, Secretaries of State, and many more—that run different parts of the executive.
Beyond that, some state high courts have held that it's unconstitutional for state legislatures to create evidence codes or codes of civil procedure, since that's a part of the judicial power; that's not the federal view. Many states provide that the governing bodies of various powerful agencies will be appointed in part by the legislature; at the federal level, that's not allowed (except as to essentially advisory bodies).
Of course, other features of state government structure are also often different from the federal. Many states elect judges, many states allow the citizen initiative, referendum, and recall. Nebraska has a unicameral legislature. Different states have very different rules as to the governor's veto and pardon powers; and the list could go on.
There are doubtless some commonalities: No state has a parliamentary system, where the Governor is elected by the legislature, though I think there's nothing in the federal Constitution precluding that. (Many local governments, I believe, have something like that sort of model, with the city council appointing a city manager.) State and federal governments arise, after all, from the same constitutional culture, and the federal constitutional rules are an influential part of that culture.
And there is probably an irreducible constitutional minimum: I suspect that judges have to have at least some level of independence from legislative or executive officials (plus of course each state is supposed to have a republican form of government, so monarchies are out, and no state can have a House of Lords because no state can grant titles of nobility). Also, while states have considerable latitude in deciding voter qualifications in some respects, that's limited in other respects (both expressly, as to race, color, condition of previous servitude, sex, and age above 18, and via the Equal Protection Clause, as to various other matters).
But "the doctrine of separation of powers embodied in the Federal Constitution is not mandatory on the States,"and there is a broad tradition of substantial state variation from that federal structure.