A (not particularly amusing) cartoon in the July 5 New Yorker has a doctor giving a bedridden patient some food on a tray and saying: "That which doesn't kill you might give you stomach trouble."
The only reason I mention it here is that its oddly stilted wording (why not say "What doesn't kill you"?) provides an example of a case where the much-fetishized but illegitimate rule about never using which to begin an integrated relative clause is obligatorily broken: not even a New Yorker copy editor would "correct" that which doesn't kill you *that that doesn't kill you.
The supposed rule is clutched like a lucky rabbit's foot by under-informed grammar pedants, as we have noted on Language Log dozens of times. When Ann Coulter using it as a literacy test for Supreme Court justices, to take a random example, is to see prescriptive grammar pontification at its stupid worst.
The rule is a fiction, invented during the 19th century by men who thought it would be nice to clean English up a bit — men like the Fowler brothers (though at least they were well enough versed in grammar to realize that the rule would have to have a whole slew of exceptions). Yet E. B. White stuffed a dogmatic assertion of the rule into The Elements of Style in 1959, and altered the text of the rest of the book to conceal the fact that his old mentor William Strunk knew nothing of it and had never obeyed it (Jan Freeman discovered this; I discuss the matter in this recent article).
One of the cases in which absolutely no one respects the rule is where an integrated (or "restrictive") relative clause — the kind that doesn't need commas at each end — is attached to that, as we just saw from the cartoon caption. But there are several others — for example, where a preposition precedes which at the head of the relative clause (nobody corrects a country with which he was thoroughly familiar to *a country with that he was thoroughly familiar). To avoid being immediately and overwhelmingly falsified by the usage of every Standard English speaker, the rule needs a complicated bunch of exception clauses.
And to get a really good match to the usage of Standard English speakers you need to drop the rule completely. What is actually true about expert users of English, when they are not being nibbled to death by copy-editing ducks, is that they use both that and which in integrated relative clauses, in proportions that aren't very far away from being 50/50. Even E. B. White ignored the rule when he was doing what he was good at — writing English, rather than writing about English.