Whether you become an American citizen by birth or voluntarily (by applying for citizenship), it gives you certain rights. On the flip side, American citizenship comes with many duties and obligations, although they are less clear-cut. (Think of it as having to work for those rights.) If you're thinking about applying for citizenship, be aware of all your rights and responsibilities.
TL;DR (Too Long; Didn't Read)
The main rights of American citizens are in the Constitution's original Bill of Rights, while duties and obligations of U.S. citizenship are less explicitly defined.
Rights of Citizenship
The Bill of Rights, part of the Constitution of the United States, contains the rights of American citizens. The First Amendment of the Constitution covers freedom of religion, freedom of speech and press and freedom of assembly. Freedom of religion is the right to practice any religion you like (or no religion at all). Freedom of speech and press is what people commonly refer to as "free speech." This covers the rights of individuals to express themselves however they choose, whether that is through online communication (e.g. blogs and social media), art, music, clothing and even actions like flag burning. The "press" part gives newspapers, radio, television stations and online sources the right to express opinions without interference or constraint by the government. Freedom of assembly gives U.S. citizens the right to to assemble peacefully and petition the government without fear of punishment.
Several of the Amendments are considered "the rights of the accused." For example, the Sixth Amendment gives the right to a prompt, fair trial by jury, and the Eighth Amendment restricts excessive fines and cruel and unusual punishment. Under the Bill of Rights, U.S. citizens also have the right to bear arms, to run for elected office, to apply for federal employment and to vote in elections for public officials. Perhaps the most important, albeit non-specific, rights are the "certain unalienable" rights contained in the U.S. Declaration of Independence of July 4, 1776: Life, liberty and the pursuit of happiness.
Duties and Obligations of Citizenship
While you won't find an explicit list of official obligations of a U.S. citizen anywhere, the U.S. Citizenship and Immigration Services provides a list of nine responsibilities, including supporting and defending the Constitution, participating in the democratic process, respecting and obeying federal, state and local laws, respecting the rights, beliefs and opinions of others, paying income and other taxes on time, and serving on a jury when called upon. Some of these are legal requirements, such as obeying laws and paying your taxes, while others are broader and more likely to be the subject of debate. For example, if participating in the democratic process is a responsibility, does that mean it is a duty to vote? Some people may say so, but it is not illegal to abstain from voting.
Relationship Between Rights and Responsibilities
The rights and obligations of U.S. citizenship should be considered as a whole, because they are all linked. You cannot exercise your rights without also being mindful of your obligations. For example, you have the right to express your opinion, but that doesn't mean you can say anything you like. You cannot shout "Bomb!" in an airport if there is no bomb. You do not necessarily need to comply with the duties that come along with being a U.S. citizen if you think they are unfair. For example, you can be punished for breaking a law, but if the law is inequitable, citizens have the power to try to change it.