Let me put this up quietly tonight in hopes that everyone is too tired to argue. 

There was some nervous tweeting among editors today about the that/which rule. You may have been taught it under various terms: Restrictive (limiting, essential, defining) relative clauses begin with that and are not set off with commas; non-restrictive (non-limiting, non-essential, non-defining, parenthetical) relative clauses begin with which and are set off with commas. You know it is a rule because your English teacher told you so, and besides, there it is in black and white in the Associated Press Stylebook

There is just one little hitch: IT IS NOT A RULE. 

The Fowler brothers suggested in The King's English that it would be a useful distinction to observe; it would tidy up the language a little. But it was a suggestion, not a rule. And later, in Modern English Usage, H.W. Fowler says that since most writers use which for both restrictive and non-restrictive clauses anyhow, the best thing to do is to pay careful attention to the commas. That advice still holds good. 

Writing last December in "A Rule Which Will Live in Infamy" at Lingua Franca, Geoffrey Pullum itemized three plain exceptions to the supposed rule:

"The putative ban can’t apply when a preposition precedes the relative pronoun: the town in which she lived is grammatical but *the town in that she lived isn’t.

"The supposed rule should be ignored when modifying demonstrative that, because that which you prefer is clearly preferable to *that that you prefer.

"The rule can’t apply to a conjoined whichWe must trust the unknown entity who or which created us is grammatical but *We must trust the unknown entity who or that created us isn’t."

The that/which distinction is more thoroughly observed in American English than in British, and I've heard people say that British constructions are confusingly ambiguous. Not ever having had much trouble sorting them out myself, I think that the problem is more American than British: People who have been too thoroughly schooled in the distinction have trouble recognizing variants. 

Moreover, since instruction in grammar and usage in this country is so erratic and unreliable, I see daily evidence, from students and journalists alike, that they have been made nervous and shy away from which clauses because all they remember is that which is somehow tricky. The result is non-restrictive relative clauses beginning with that and not set off with commas. Not the thing. 

Now, before you start to accuse me of pulling down the pillars of the temple on our heads, the that/which distinction is perfectly serviceable most of the time. But there's no need to make a damn fetish of it. Just make sure the commas go where they belong, and all will be well.