Like many others, I have a profound respect for correct use of the poor apostrophe. I’m going to take the issue a step further, however, and complain about a very particular pet peeve of mine: the flagrant misuse of correct punctuation marks when setting type. Even when you know the usage rules, you still have to know which marks are correct. I have seen all sorts of professional typesetting in books, posters, ads, and all kinds of other junk where no one ever thought to notice that a real apostrophe, or real quotation marks, were not being used. (Yes, it's hard being this anal-retentive, but my friends have learned to love me anyway.)
So I offer my own contribution to your pool of grammatical knowledge: Sparky's Typesetting School, Lesson One:
Apostrophe/Single Closing Quote
The one, the only. Note that the open end of the apostrophe faces left — always. If it does not, it's a single open quote (see below). In typefaces where the apostrophe does not have such a curlicue shape as the one shown, it will still be heavier at the top, taper toward the bottom, and lean toward the right.
Single Open Quote
The companion to the single closing quote. This is only used when there is a quotation within a quotation. Contrary to the results you may get when using the smart quotes feature in most software, this is not what is used when you refer to the '90s, or in other cases where an apostrophe follows a word space.
Used to denote measurement in feet, or time in minutes. These days, no one will care much if you use a neutral single quote for this (which has no slant, see below), but it is not actually correct.
Single Neutral Quote
Technically, this should only be used for programming code. It's not an apostrophe, it's not a prime, it's not a single quote. It was developed for typewriters. This is what you get when you use simple HTML or you don't use the smart quotes feature and you try to type an apostrophe. It's wrong. (I let this slide in HTML because it's a pain to key in the proper code all the time.)
Double Open Quote
Opens to the right, and should definitely be used instead of a double neutral quote (see below).
Double Closing Quote
Opens to the left, and should definitely be used instead of a double neutral quote or a double prime (see below).
Used to denote measurement in inches, or time in seconds. These days, no one will care much if you use a double neutral quote for this (which has no slant, see below), but it is not actually correct.
Double Neutral Quote
Technically, this should only be used for programming code. It's not a double open or close quote, it's not a double prime. This is what you get when you use simple HTML or you don't use the smart quotes feature and you try to type a double quote of either kind. It's wrong. (I let this slide in HTML because it's a pain to key in the proper code all the time.)
For more information, you may want to pick up the very excellent Words Into Type, your preferred style manual, or even the simple-but-classic The Mac Is Not a Typewriter (or you can use The PC Is Not a Typewriter so you learn the right keyboard shortcuts).
Future nits to pick: hyphens and dashes, the ellipsis, and punctuation and font changes.