Constitutional rights are those rights which are described in the Federal Constitution, and the constitution of your state. Your constitutional rights are your strongest protection against improper police conduct, and wrongful conviction. Most constitutional rights were composed in reaction to specific abuses by British authorities, during Colonial times. The rights described in the Federal Constitution must be observed by all agents of the federal government.
Most, but not all, of the rights listed in the "Bill of Rights" (the first ten Amendments to the Federal Constitution) have been "incorporated" to the states through the Fourteenth Amendment, meaning that the State must respect those rights as well. (The Fifth Amendment's "Right to Indictment by Grand Jury," and the Eighth Amendment's protection against "Excessive Bail," are not "incorporated to the states," and thus do not have to be observed in state prosecutions.)
Article 1, Section 10 of the U.S. Constitution
No state shall enter into any treaty, alliance, or confederation; grant letters of marque and reprisal; coin money; emit bills of credit; make anything but gold and silver coin a tender in payment of debts; pass any bill of attainder, ex post facto law, or law impairing the obligation of contracts, or grant any title of nobility.
The protection against "ex post facto" laws means that the State cannot pass a law after a person has committed an act, and then prosecute the person for the prior act. You can only be prosecuted under the laws that are in effect at the time of your act. The protection against "bills of attainder" prevents the State from passing a law meant to punish a specific individual without judicial process.
Fourth Amendment Rights
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
The Fourth Amendment provides general protections against arbitrary search and seizure of persons and property. While there are many exceptions to the Fourth Amendment "warrant requirement," it does provide broad protection of the general public from inappropriate police conduct.
Fifth Amendment Rights
No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
The Fifth Amendment provides a number of protections that we take for granted. The protection against "double jeopardy" (being tried more than once for the same offense) arises from this Amendment. Similarly, the right to remain silent emerges from a defendant's Fifth Amendment right not to be compelled to be a witness against himself. The Fifth Amendment also provides a broad right to "due process of law." Your "Miranda Rights" come from the Fifth Amendment.
Sixth Amendment Rights
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the assistance of counsel for his defense.
The most important Sixth Amendment rights for criminal defendants are the right to assistance of counsel, the right to compel witnesses to appear at trial, the right to cross-examine ("confront") witnesses at trial, the right to trial by jury, and the right to be informed of the nature of the charges that have been filed against you and of potential punishments. Also of significance is the right to a speedy trial which, although frequently waived by defendants, prevents the state from incarcerating defendants for years while their trials are perpetually delayed - a problem that is common in some other countries.
Eighth Amendment Rights
Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
The Eighth Amendment prohibits excessive bail in federal prosecutions, and bars excessive fines and cruel and unusual punishments in all prosecutions.
Fourteenth Amendment Rights
Section 1. All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
The first Section of the Fourteenth Amendment's most important provisions require that all citizens be granted "equal protection" of the laws. This means that the State and Federal governments cannot deprive an individual or class of people of the rights enjoyed by other persons who are similarly situated. The Fourteenth Amendment also bars the States from violating the "privileges and immunities" of Citizens of the United States. The Fourteenth Amendment expressly extends Due Process rights to state prosecutions, and it is through this clause that the majority of the rights listed in the "Bill of Rights" have been incorporated to the States.
For the most part, the rights described in state constitutions usually resemble those in the Federal Constitution. However, many states have provisions which offer broader protections than the Federal Constitution. For example, some states hold that their residents have an "expectation of privacy" in their garbage, meaning that the government must have probable cause to search garbage. Some states hold that traffic "check lanes," where entire lanes of drivers are stopped and checked by the police, are unconstitutional. The United States Supreme Court has held that the Federal Constitution does not recognize an expectation of privacy in garbage, and that traffic check lanes are constitutionally permissible.
States can only add to your Federal constitutional rights -- they cannot pass constitutional amendments that restrict the rights you receive under the Federal Constitution.