While Magna Carta has been largely stricken from the legal rulings of the United Kingdom since 1965, the charter continues as an idealized cornerstone of English Common Law. What was once a simple contract between King John and his barons in 1215 has turned into an example of universal rights and "due process". Most of this comment will focus in on what most would consider the "key" chapter of the charter, Chapter 39 (number 29 in the 1225 version):

No freeman is to be taken or imprisoned or disseised of his free tenement or of his liberties or free customs, or outlawed or exiled or in any way ruined, nor will we go against such a man or send against him save by lawful judgement of his peers or by the law of the land. To no-one will we sell or deny of delay right or justice.

By the 15th century, Magna Carta was not often cited in legal codes, other than the occasional textbook for learning lawyers. The "great letter" certainly had protections for English landholders, but other laws were given precedence, even with Edward III's 1369 Statute saying that any law that counteracted the charter "shall be holden for none." However, Magna Carta still existed as a piece of legislature that embodied "due process"--a shining example of laws that applied to king, Parliament, and everyone.

Mentions of Magna Carta as a means of protecting individual liberties usually arose when an English monarch threatened Parliamentary supremacy. As Ralph Turner explains in his history of the document's impact on law, lawyers and Members of Parliament rekindled their interest in Magna Carta during the eras of James I and Charles I, making the charter "a key element of England’s ‘ancient constitution’, a body of laws and customs supposedly surviving from pre-Roman Britain that imposed limits on the king’s power over his subjects."

By the 1640s, Edward Coke wrote his meditations on English law, going so far as to call Chapter 39 of Magna Carta a "roote" from which "many fruitfull branches of the Law of England have sprung," including personal rights and due process. Whigs later reinterpreted Magna Carta, especially Chapter 39, as a document outside of legal hierarchy, a superseding legislation that applies to all Englishmen.

In North America, aspiring lawyers had their own copies of Coke's comments on English law, including his sections lauding Magna Carta's supremacy in Common Law. John Adams read Cicero and Coke extensively, to serve as an example; lawyers and legislators in the future United States revered Coke, and Magna Carta. Massachusetts' state seal highlights American colonists' opinion of Magna Carta; the Massachusetts man wields a sword and Magna Carta, the embodiment of his rights.

After American independence, the idea of an extra-hierarchical document that applied to all peoples became a Constitution--a work of law that only could be touched by a Supreme Court. Americans shared what Turner calls a "near-religious veneration" for Magna Carta and its legal protection. By 1791, the Bill of Rights paraphrased Chapter 39, saying no one may be "deprived of life, liberty, or property without due process of law.'"

Obviously, Magna Carta, an English document, does not come up as a direct precedent in an American courtroom. And in the United Kingdom, a 1965 Law Commission statute gutted most of Magna Carta for being inapplicable to modern English law (except for a few chapters, including Chapter 39). Nevertheless, legal historians and lawyers still cite the charter as a symbol of due process and legal protection from an aggressive executive power, even if only in our rhetoric.

Sources: Ralph V. Turner, The Meaning of Magna Carta Since 1215. History Today. Here.

Edward Coke's comments on chapter 39

For a large but decent compendium on English (and American) legal tradition, try Robert Langbein's History of the Common Law: The Development of Anglo-American Legal Institutions. It contains a chapter on early English law and Magna Carta, as well.