As you saw with the explanation of federalism, state governments, while subject to an overseeing control of the federal government, are endowed with their own rights. And remember that under the 10th amendment to the Constitution, any rights not given to the federal government specifically belong to the states and the people.
All states have a constitution, almost all of which follow a format very similar to the federal constitution. Therefore, all states have executive, judicial and legislative branches.
Like the Federal government, state governments have steadily changed to define state and citizen's rights, reduce spending and improve representation of the people. One of the greatest times of change was in the early 1900's during the Progressive Movement. In this time, corruption and misuse of political power came under fire by groups wanting to limit the power of boss controlled political systems. Though not entirely successful, some of the Progressive Era reforms to be initiated included:
The Secret Ballot - this made it harder to pressure or manipulate individual votes
The Initiative - this allowed voters to petition for proposed laws
The Referendum - this allowed voters to decide about bills and constitutional amendments
The Recall - a legal way for citizens to remove elected officials from office
The Direct Primary - allowed the voters, not the party leaders, to select candidates for office
In addition, the Seventeenth Amendment was passed in 1911, which gave the power to elect Senators to the people of the state, not the leaders of the state.