Why don’t we approach this question from a different perspective? Granted, there’s scads of cases out there dealing with constitutional law, civil rights, and so on. But what are the Top 10 cases that a well-informed American citizen should know about, either because 1) they come up so frequently in conversations and political discussions, or 2) they are foundational in nature.
So, I propose that we all put forward suggestions for cases that we think are the 10 most important. Everybody can comment on other peoples’ suggestions. If we can reach a consensus, then we will have the “SDMB Top 10 Supreme Court Decisions™”!
Three parameters for suggestions:
First, don’t just give a cite; you have to explain why it should be on the list.
Second, I’d say the list should normally only include cases that have not been overruled or overturned by constitutional amendment, but I’d make at least one exception: Dred Scott, because of its historical importance to the Civil War.
Third, I’d be reluctant to put any recent cases (say, within the past 10 years) on the list because they’re still too close. There’s over two centuries of decided cases, so excluding the last ten years just adds historical perspective.
Here’s some suggestions that came to me. I’ve only given eight, to allow myself a bit more time for reflection.
I think the number one case is obvious: Marbury v. Madison, 1 Cranch 137 (1803), the grand-daddy of constitutional law. Established the basic principle of judicial review: that the courts have the authority to hold that a federal statute is unconstitutional if it does not comply with the federal Constitution.
I’m not that familiar with pure federalism cases, so I’m going to skip straight to Dred Scott v. Sandford, 19 How. 393 (1857), the second time the Supreme Court held a federal statute unconstitutional. The holding, that Scott was still a slave, galvanised a lot of popular opinion on the slavery issue immediately, but the reasoning of the Court, which essentially held that the federal government could not prevent slavery from spreading into the western territories, had serious long-term implications that contributed to the outbreak of the Civil War. Overturned by the 13th, 14th, and 15th Amendments, but still a crucial case to understand constitutional developments.
Third on my list would be Palko v. Connecticut, 302 U.S. 319 (1937). This case is key because it adopted the principle that the 14th Amendment had selectively incorporated parts of the Bill of Rights and applied them to the states. That decision drastically expanded the scope of federal court jurisdiction to review state actions, and paved the way for all the criminal procedure cases and freedom of speech/establishment of religion cases.
Fourth on my list would be Brown v. Board of Education, 347 U.S. 483 (1954), which held that “separate but equal” schools for blacks and whites were unconstitutional under the 14th Amendment. The case started the ball rolling for desegregation, and also set the stage for a lot of the latter civil rights cases.
Fifth on my list would be a less well-known case, but essential to understanding the constitutional principles governing criminal cases: Mapp v. Ohio, 367 U.S. 643 (1961). In this case, the Court held that the exclusionary rule was not simply a rule of the federal courts, but constitutionally mandated. It therefore applied in all criminal cases, whether in the state or federal courts, where a constitutional right had been infringed in the course of a criminal investigation/prosecution. The case itself is not well known, but the point of law is the staple of Law and Order, which really is all that is needed to justify inclusion on the list. 
My sixth case is Baker v. Carr, 369 U.S. 186 (1962), dealing with voting rights. The Supreme Court held that the failure of the State of Tennesee to re-apportion seats in the state house for over 60 years, notwithstanding the major population shifts from the rural areas to the urban areaa, deprived citizens in the urban areas of their equal right to vote. This case was also crucial to the civil rights debate, since it helped to break the white stranglehold on the state governments in the south. One reason I would include it on the list is because Chief Justice Warren, on his retirement, said that it was the most important case that came before the Court during his time as Chief Justice, not Brown or any of the other landmark cases.
Seventh on my list is the well-known case of Miranda v. Arizona, 384 U.S. 436 (1966). It elevated the principle of police warnings to detainees in criminal cases to a constitutional requirement, a significant constitutional development, with wide-ranging impact on all state and municipal police forces. (It also qualifies under the Law and Order corollary.)
Eighth on my list would be Roe v. Wade, 410 U.S. 113 (1973). True, as kunilou comments, in terms of legal principles, it built upon the principles set out in Griswold v. Connecticut, 381 U.S. 479 (1965), but in terms of immediate and long-term impact on the political debate in the United States, Roe is one of the most significant. Presidential candidates’ positions on abortion and Roe have become a touchstone for a lot of voters, and the entire issue of appointments to vacancies on the Supreme Court looks back to Roe.
That’s all for now. (Oh, and but for the 10 year rule, I’d be inclined to cite Lawrence v. Texas, both for its significance for gay and lesbian equality, and for its substantive due process analysis.