Without looking at the responses or anything else, for that matter
Roe v. Wade
Brown v. Board of Education, Topeka, Kansas
Those two leaped immediately to mind.
FaerieBeth (female teacher)
I was hoping this would come up! Permit me to add Egan v. Canada, M. v. H., Little Sisters v. Canada, and Reference re. Same-Sex Marriage.
Presault v Vermont, the Supreme Court affirmed the constitutionality of the Federal Rails to Trails Act.
Oh and, for heaven’s sake, Morgentaler v. The Queen.
If you’re wondering:
M. v. H.: same-sex couples can become common-law spouses the same as opposite-sex ones.
Egan v. Canada: S. 15 of the Charter includes sexual orientation as a prohibited grounds of discrimination.
Little Sisters v. Canada: obscenity customs laws violate freedom of expression but are saved under S. 1 of the Charter.
Reference re. Same-Sex Marriage: the federal government may recognize same-sex marriage as marriage.
Okay, kind of specialized, but come on, Egan’s pretty much the basis of all subsequent jurisprudence on the question. Then there’s Vriend v. Alberta, that provincial human rights acts must include sexual orientation as prohibited grounds, and more broadly that a law can be unconstitutionally discriminatory by what it omits as well as by what it includes.
R. v. Morgentaler: abortion is legal. (Morgentaler v. The Queen is actually a different case from 12 years earlier with the opposite result, being before the introduction of the Charter. Yes, it’s the same Morgentaler; he recently received the Order of Canada.)
Roe v. Wade
District of Columbia v. Heller
Dinsdale v. Moose
Good calls, Matt. Yes, those are significant SCC cases too. Good to have them added.
Aside to Hypnagogic Jerk: No, I’m not a lawyer–yet. I’ve finished law school and am working towards my bar admission, so I’m kind of in limbo–I know more than the average layperson, but not enough to be a lawyer. 
Anyway, Constitutional Law was among my favourite courses at law school, so those cases are some of many that were of interest to me, and fairly fresh in my mind besides.
what, no love for Reference re Chemicals?
Heh heh heh… good times. And don’t fret – the other party was the United States, so it’s “Blockburger v. U.S.” Most casual references to it are simply “Blockburger,” so you’re good.
And I can’t tell you how pleased I am that you remembered that!!
I think there’s a difference between “name two cases” and “name two cases you disagree with.” I might pause for thought on the latter, and I would humbly aver that I know a few Supreme Court cases.
The problem is – what does “disagree” mean? Is the questioner asking about cases where I dislike the result, but accept it was either compelled by law, or accept that a good-faith analysis of law could lead there? Or the opposite – I agree with the result as a matter of wise social policy, but disagree about the legal analytical process used? Or must both be present? What about older cases, where I may have cavilled at the time, but whose results are now so entrenched that changing them would upset so much decisional law that I accept them now?
I think Lawrence v. Texas was poorly decided, on bad rationale, but I agree with the result. I think Lago Vista was correctly analyzed, but I don’t like the result. Miranda was poorly decided and reached a poor result in its time, but has now generated such progeny in case law that it’s unassailable. And Roe, virtually standing alone, was poorly decided, reached a poor result, and can still be disposed of today without upsetting the precedential applecart.
So the neutral question Name two cases… is something that should pose no problems for any reasonable person.
Name two cases you disagree with? That requires clarification, at least.
Or the noted British criminal case from the late Sixties, R. ex. rel. Dinsdale v. Piranha.
Sure, right from this thread.
Bush v Gore
Plessy v. Ferguson
I would not have agreed with one of your two choices, and in any event, you don’t say how you reached this conclusion. Is it that you don’t like the results in both cases, but you agree the Court analyzed the law correctly? (In other words, what’s needed is a change in the law…) or is it that you feel the Court improperly analyzed the law? And if the latter, in either case, what specific errors of law did the Court commit?
Well, I think you and WhyNot are suggesting a level of sophistication that I feel is indeed rare in American political discussion. And of course, if the question is unclear, the politician could ask for clarification.
But far more likely, I would expect most any candidate for office above dogcatcher to have little difficulty going into some spiel about how he/she disagrees with “the recent decisions showing a trend towards” any number of liberal or conservative issues. And such a response would not have caused anyone to raise an eyebrow.
Hell, in my (appellate) experience it is nearly ALWAYS sufficient in court to simply refer to a legal precedent/principal, without needing to provide a specific name or citation. And at argument I can always simply say the citation is in my brief. (Always cracks me up in TV shows where a lawyer just pipes up Smith v. Barney, as tho the name alone were sufficient to make his point. Of course, in all practice areas there are the baseline cases whose names serve as useful shorthand.) There would be no problem with a candidate saying they forget a case’s name, but providing general info to indicate that they are familiar with at least some basic aspects of the dispute. And in Palin’s case, she could always say, “I’ll try to find some and get back to ya!” 
I try to give those guys the benefit of the doubt, and assume their obscure case names, sans cite, are well-known in their jurisdictions. And as you say, there are some cases that are so well-known as to stand for certain propositions that they get tossed around as synonyms for the principle: Strickland, Batson, Blockburger, Edwards, Miranda, are all shoo-in references for their respective issues.
Also love it when the atty just shouts out “Objection” without identiying any gorunds. 
Ehr… the Roe-whatever one re. abortion and, uhm…
uh…
that’s it.
The other US case I remember the name of is Miranda and IIRC that was California.
OTOH, I can tell you several cases from the Spanish Constitucional!
The moose bit my sister.
My 5’2" 100-pounds-soaking-wet sister is nicknamed Moose.