Knowing the names helps establish communication, and is therefore good. It even allows for coded communication as in 2000 with Bush mentioning Dred Scott instead of Roe.
I was kidding about the Court of Exchequer analogy, if my sarcasm wasn’t evident. The United States is one of the few countries where the judicial branch is truly a separate branch of government. Constitutional decisions cannot be overturned by an act of Congress like court decisions in England can be by the House of Lords. To understand our current politics, you have to understand a handful of key Supreme Court decisions (whether by name or content). Consequently, we learn a lot of these decisions in school and they are central to a lot of our political discourse in a way that is pretty unique to the U.S.
I thought it must be something like that. Cheers.
Without looking at the thread.
Roe Vs. Wade.
Brown Vs. Board of Education…I think it’s Brown.
Knowing (or at least being able to recognize) the names is important for the same reason that being conversant with major works of literature is important; people will allude to them. Saying that something is “like Plessy v. Ferguson” is the same thing as saying, I don’t know, “That guy’s no Solomon!” It’s common knowledge for the educated American, at least, and something it’s good to be conversant with to understand allusions, if not to understand important rights and such.
Printz v. United States
Buck v. Bell
Buttered mammals. Mmmm.
Roe v Wade is the only one I know and I had no idea what it refered to. So in answer to the op - yes I can’t.
My apologies. I should have limited the OP to U.S. adults.
Damn! I was just coming in here to mention that one! Oddly enough it was the first case to pop into my head upon reading the thread title. 
Oh, and another recent and somewhat controversial case nobody’s mentioned yet: District of Columbia v. Heller.
Another damn foreigner here. I got Roe v Wade but my second example – which I remembered as that monkey evolution school thing – wasn’t in the Supreme Court. It was actually Scopes v. State, 152 Tenn. 424, 278 S.W. 57 (Tenn. 1925.
Goodness, I don’t think many of us know it by that name. Over here, it’s “The Scopes Monkey Trial”. Seriously. (But yes, not SCotUS.)
That’s odd that everyone is saying Brown v. Board of Education; for some reason I wouldn’t have even thought of that one. (I immediately thought of Roe v. Wade and Marbury v. Madison.)
Valete,
Vox Imperatoris
The SDMB has a don’t be a jerk rule. There is nothing about Pennoyer that is not jerkish.
Gertz v. Welch
New York Times v. Sullivan
Cohen v. California
Earlier posters got all the obvious ones.
It had never occurred to me before this instant how absurd that is. Seriously, “Scopes Monkey Trial”?
My personal favorites:
Muller v. Oregon
Lochner v. New York
Double Points for whoever knows why Muller v. Oregon is famous, and how it relates to Brown v. Board of Ed. (No cheating now!)
The famous ones:
Marbury v Madison
Roe v. Wade
Gore v. Bush
Plessy v. Ferguson
Brown v. Board of Ed
I thought of Title IX first off but can’t remember the case name… checks ah. Franklin v Gwinnett County Public Schools.
Affirmative Action (UC v Bakke).
Planned Parenthood v Casey.
Then Plessy v Ferguson.
Then Lawrence v Texas.
The People vs Larry Flint
Miller v. California
Hustler Magazine v. Falwell
Escobedo v. Illinois
McCulloch v. Maryland
It was a demeaning nickname, you know, “He says that people come from monkeys, instead of believing in the true word of God.”
Valete,
Vox Imperatoris