Early political thinkers such as Plato or Aristotle and their political beliefs can be the topic of your research. Research their theories on how society should be structured and compare and contrast their ideals. Another option can be to choose one of these thinkers and analyze how their theories have influenced our political system today. Many different topics can surface when considering early political theory.
The Constitution is the highest law of the United States and all other laws must be in accordance with it; the interpretation of this document has led to much controversy over the years. Research the controversies such as a loose versus strict interpretation, or the idea that the constitution should be modified to fit more present-day ideals. Research how the role of the President, Senate and Congress has either changed or stayed the same in accordance with the Constitution.
Researching and analyzing a president's time in office is applicable to most political science courses. You can compare the amount of power one president had compared to another and note a trend toward or away from imperial presidencies. You can analyze each president's war and peace strategies and explain the pros and cons. Research specific policies a president influenced in relation to your course. For example, if your class is about America during the post-Civil rights era, research Ronald Regan's views and policy influence.
There are an abundance of historical events involving both domestic and international politics. Researching historical events can lead to varies paper topics. Researching World War II can lead to an analysis of Hitler and his Nazi party, or international relations between America and its allies. Compare and contrast the cause, effects and recovery strategy for the Great Depression in the 1930s to the early 21st century economic depression.