The first two that come to my mind are:
Roe vs. Wade
Dred Scott vs. Sandford
Looking back over the thread, there are many I don’t recall at all. This includes Gideon v. Wainwright which I should recall and I remember a movie about Gideon.
I also do not remember Marbury v. Madison & Plessy v. Ferguson.
It was the first example of the use of sociological jurisprudence as argument through a “Brandeis Brief,” the same legal theory that Marshall would use when he argued Brown. 
Without cheating, I suspect that these have been most people’s two too:
Brown vs. The Board of Education
Roe vs. Wade
(Why am I suddenly having Family Feud flashbacks?)
Goldman v. Weinberger.
That’s the one, thanks.
Oh, thank goodness it’s not just me. The names are familiar but the memory is coming up with 'nuttin.
Dredd Scott and Miranda would have been #3 and #4 for me, though. (After some thought.)
I’m in law school, so I don’t count. But sticking to cases I had heard of before law school:
Mapp v. Ohio (secondary searches)
I took an undergrad course in antitrust economics, so U.S. v. Standard Oil, U.S. v. DuPont, and all those chestnuts. Berkey v. Kodak was briefly relevant to one of the Microsoft cases (at least according to my term paper).
Plus the usual suspects: Roe, Marbury, Brown.
Marbury v. Madison
Kelo v. New London (because I have a coffee mug on my desk with a quote from Justice Thomas’s dissent: “Something has gone seriously awry with this Court’s interpretation of the Constitution”)
Yep, for me Brown and Miranda would have been 3 & 4 and after that I don’t even think I know the names of any other cases from memory.
Seems amazing any reasonably intelligent American could not come up with - at least - Roe and Brown.
I could probably name/describe 30 or so without breaking a sweat, but I kinda have an advantage in that area. From memory, I think the brief I drafted yesterday cited Pierce v. Underwood, Commissioner INS v. Jean, and Hensley v. Eckerhart. Maybe Sullivan v. Finklestein and 1 or 2 others, but I’m not sure.
Can I be vice-president or do I have to shoot a moose first?
The test for attorneys is a little different. It mostly involves math.
That’s going to be rough. If I was any good at math, I’d be a doctor, not an attorney.
But shooting an attorney in the face is another way to establish your bona fides, right? 
That’s why the IP folks get paid so handsomely.
Only if you then get that attorney to apologize to you for being shot.
Well done Pravnik! Of course, you being an attorney, I expected nothing less… 
I wrote my major US History term paper on Louis Brandeis and how the Brandeis brief was a culmination of his lawyering career, but not particularly novel for him. Eight years later, I’m still proud of it.
Perhaps not in some governor’s minds…
TBH, I could only come up with Roe vs. Wade. So, I’m eligible to be VP candidate.
Attorneys can do math. But watch how they do it: they put a in front of all the figures while working the problem, and then take it out when done, unless it actually refers to , in which case they keep all the $.
In the Quayle years, the joke was that the Veep thought Roe v. Wade was a consideration of methods of crossing the river.
Off the top of my head I came up with:
Roe v. Wade
McCulloch v. Maryland
Strickland v. Washington
D.C. v. Heller
Schechter Poultry v. U.S.
Youngstown Sheet & Tube v. Sawyer
Bush v. Gore
Marbury v. Madison
Korematsu v. U.S.
U.S. v. Nixon
Loving v. Virginia
Lawrence v. Texas
Bowers v. Hardwick
Gideon v. Wainwright
Mapp v. Ohio
…and a bunch more I know by the name of only one party, like Carolene Products.
Roe Versus Wade is the only one I know.