The Declaration of Independence lists life, liberty, and the
pursuit of happiness as unalienable rights. The Constitution lists
certain rights, but they aren't unalienable. For instance, the
second amendment grants one the right to bear arms, but someone who
is convicted of a violent felony or who is mentally unstable may be
denied the right to purchase and possess guns. The wording of the
Declaration of Independence draws heavily from the French
Revolution, where the battle cry was liberty, equality, fraternity.
Equality, however, was especially problematic for the signers of
the Declaration of Independence, as many of them owned multiple
slaves. This continued to be a problem at the Constitution
Convention, where 28 of the 55 delegates had multiple slaves, some
having slaves numbering in the hundreds.
I believe you are referring to the first sentence within the
second paragraph of The Declaration of Independence, which reads
(bold emphasis is mine):
We hold these truths to be self-evident, that all men are created
equal, that they are endowed by their Creator with certain
unalienable Rights, that among these are Life, Liberty and the
pursuit of Happiness. That to secure these rights, Governments are
instituted among Men, deriving their just powers from the consent
of the governed, That whenever any Form of Government becomes
destructive of these ends, it is the Right of the People to alter
or to abolish it, and to institute new Government, laying its
foundation on such principles and organizing its powers in such
form, as to them shall seem most likely to effect their Safety and
Happiness. Prudence, indeed, will dictate that Governments long
established should not be changed for light and transient causes;
and accordingly all experience hath shewn, that mankind are more
disposed to suffer, while evils are sufferable, than to right
themselves by abolishing the forms to which they are accustomed.
But when a long train of abuses and usurpations, pursuing
invariably the same Object evinces a design to reduce them under
absolute Despotism, it is their right, it is their duty, to throw
off such Government, and to provide new Guards for their future
As this document was issued by the Continental Congress before the Revolutionary War, these sentences provide no specific guarantees to American citizens, but the point can be made that these words clearly express the founders intent. The statement also notes that these rights are bestowed by "the Creator", and not by government.
As far as the constitution goes, there are ten rights enumerated in the Bill of Rights, which are the first ten amendments to the Constitution of The United States; the Bill of Rights are:
• First Amendment - Establishment Clause, Free Exercise Clause; freedom of speech, of the press, Freedom of Religion, and of assembly; right to petition.
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
• Second Amendment - Militia (United States), Sovereign state, Right to keep and bear arms.
A well regulated Militia, being necessary to the security of a free State, the right of the People to keep and bear Arms, shall not be infringed.
• Third Amendment - Protection from quartering of troops.
No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.
• Fourth Amendment - Protection from unreasonable search and seizure.
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.
• Fifth Amendment - due process, double jeopardy, self-incrimination, eminent domain.
No person shall be held to answer for any 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 offence 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.
• Sixth Amendment - Trial by jury and rights of the accused; Confrontation Clause, speedy trial, public trial, right to counsel
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 where in 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.
• Seventh Amendment - Civil trial by jury.
In suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise re-examined in any court of the United States, than according to the rules of the common law.
• Eighth Amendment - Prohibition of excessive bail and cruel and unusual punishment.
Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
• Ninth Amendment - Protection of rights not specifically enumerated in the Bill of Rights.
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
• Tenth Amendment - Powers of States and people.
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.