Apostrophes are used in 3 cases:
1. To take the place of a letter in a contraction. is not = isn't, the apostrophe takes the place of the o we are leaving out. Included in this rule are constructions like the '70s. The apostrophe takes the place of the 19 we leave out, and we don't add an apostrophe before the s because this rule overrules rule #3.
2. To show ownership in NOUNS! NOT pronouns. Possessive pronouns, as DanQ pointed out, are a different class of word. Jimmy's book, for Fuck's sake.
3. To pluralize numbers and letters and such when they are used as words: I got all A's and B's, a movie filled with 11's. Without the apostrophes, you got all As and BS. LOL You would use this rule if you actually said 1970's, because you didn't already use your apostrophe to take the place of the 19, so it would follow this rule, not #1.

EDIT: 12 years of Catholic school, an English degree, and 30 years of teaching English: I'll go toe to toe with anyone in a grammar throwdown.

That would be rule #1, except the apostrophe is doing a twofer, covering for the o and the u in "you all."

Rule #3.

Money. Like "It's been good to see you."

I guess Uncle Pinball's Podcast could do a grammar episode.
D'oh! Is that SPAM? Will I get frozed again?