This started in james_nicoll's post here, but I like the idea, so I'm going to run with it. This is primarily for Americans (as defined broadly--citizens, naturalized aliens, illegal immigrants...anybody who would have a reason to particularly care)...

From memory, without references, how many Amendments to the United States Constitution can you identify/explain?

There are 27. It's enough to give what the Amendment is commonly referred to as. (Except that you can't say the First Amendment is "the First Amendment" or the like, of course.)

Bonus points for identifying/explaining Articles of the Constitution itself. There are 7 of those. There are also some particularly important Sections of those Articles, and indeed some pretty major Clauses--just knowing what they are and what they do, no need to number them.

Here's my list:

1: Freedom of speech and the press, peaceful assembly, separation of church and state.
2: Right to bear arms.
3: No quartering troops in private homes.
4: No unauthorized search and seizure, no warrants without probable cause.
5: Right against self-incrimination, right to due process, right to compensation for takings.
6: Right to counsel.
7: Right to speedy trial and a jury of peers.
8: No cruel and unusual punishment.
9: Everything else is to the states.
10: This doesn't mean nothing else is a right. (I may have swapped 9 and 10.)
11: Immunity--states can't be sued. (Though apparently that means the exact opposite, now.)
12: ...I think this has to do with how the President and Vice-President are elected.
13: No slavery.
14: States can't infringe on rights guaranteed by the Constitution. ("Privileges and Immunities" and "Rights of Citizenship" both being eviscerated, that's done through due process.)
15: Voting rights.
16: Income tax.
17: I think this is what made Senators directly elected, not picked by state legislatures.
18: Prohibition.
19: Women's sufferage.
20: ...no idea.
21: Repeal of prohibition.
22: Did this move Inauguration Day?
23: No idea.
24: No idea.
25: Presidential Succession, vacancies.
26: I think this lowered the voting age to 18.
27: I think this forbade Congress from voting itself pay raises mid-Term.

I have some idea on 24 of 27, I'm unsure on 7, and I probably missed details of a few more. Not bad, but not great. Then again, I'm in law, we live and die by citation and reference material.

Article I: Defines how Congress works. How old, how apportioned, how elected...Section 8 outlines the powers Congress has (what it can do). Clause 8 of that one's important to me--it's the "promote the progress of Science and the Useful Arts by securing to Inventors limited exclusive Rights" clause, AKA the "intellectual property" clause. The most important clause, though, is the Interstate Commerce clause, giving Congress the right to regulate interstate commerce. Also, the "necessary and proper" clause at the end, a catchall.

Article II: Defines the Executive. How old, how elected, powers.

Article III: Defines the Judiciary, being the Supreme Court and whatever other courts Congress creates; defines the Supreme Court's jurisdiction.

Article IV: I believe this includes rules such as Ex Post Facto and treason, but I'm not sure. That could be VI, while IV might be how laws actually get passed (if that's not part of I and II). Or VI could be how laws are passed...dunno.

Article V: Most important element is the Supremacy Clause--which says that Federal laws trump State laws if they conflict. (It does not, and I've had this argument a couple of times, say that the Supreme Court gets to make laws unconstitutional. Justice Marshall did that.)

Article VI: See my description of IV.

Article VII: I noticed this in passing, so it doesn't really court, but then neither does the section--it's a list of signatures and ratifications. Not really an active Article.

So. Seven Articles, I know three pretty well, one I know the most important part of, two I'm much more shaky on, one barely courts. I know some a couple of significant Sections and Clauses, too. Again, not great--I bet that I could memorize the whole thing with a bit of work, but haven't done so--but not awful, I think.

Oh, and I can recite the Preamble, but that's a cheat--see music line.