[moogabi]

I believe I have used the apostrophe when writing 1960s, etc. Good to know the rule, even though I'll need to get used to no apostrophe looking right. Does the same rule apply when abbreviating 1960s as 60s. In this case, would an apostrophe go before the 6, thus '60s?

[yebyen]

Apostrophe has two uses as far as I know... one is for elision ('60s indicates that "19" has been elided or omitted) and possession (The 1910s' greatest author was Franz Kafka)

The "grocer's apostrophe" or "grocers' apostrophe" is what's incorrectly added to the plural form like what you're describing, the short answer is yes. '60s not 60's.

[btilly]

Single quotes have another use. Which is to mark off quotations inside of quotations.

Technically speaking you use single quotes there, but not apostrophes. However I mention it because the quotation mark that you used is a single quote.

[yebyen]

Thanks. My keyboard only has one apostrophe/single quote key, as I suspect most do, but I have been learning to use the compose key and I appreciate little details like that.

[aestra]

The apostrophe has three uses:

    To form possessives of nouns
    To show the omission of letters
    To indicate certain plurals of lowercase letters

Rules and examples (including the decade examples): http://owl.english.purdue.edu/owl/resource/621/01/