The grade school I attended didn’t believe in teaching English grammar, so I remained blissfully unaware of all those rules everyone else seems to have had crammed down their throats. It doesn’t seem to have hurt me one bit, although it did make things difficult in foreign language classes where teachers suddenly expected students to know the difference between a gerund and a present participle. (I wish that my school had offered descriptive linguistics as an alternative.) It was at college that I encountered “language police” for the first time. It wasn’t my professors, but other students — unfortunate victims of proscriptivism. I still remember being criticized for using “that” with a nonrestrictive clause.
Comforted by my Freshman English professor that the supposed error was a matter of stylistic choice, I continued to ignore the “that vs. which” rule. Until I installed Micro$oft Word, that is. From then on I found myself consistently hounded by my word processor for my failure to apply this rule. I began to lose confidence in my own grasp of English grammar and began to conform.
Fortunately, Arnold Zwicky has restored my grammatical confidence, He quotes H. W. Fowler, who in 1926 wrote: “it would be idle to pretend that it is the practice either of most or of the best writers.”
In any case, Merriam-Webster’s Dictionary of English Usage details the sad history of this “rule”, noting wryly that authors who recommend it routinely violate it and that the facts of usage are squarely against it. MWDEU concludes, “You can use either which or that to introduce a restrictive clause–the grounds for your choice should be stylistic” (as it was for Bellow), and adds, “Formality does not seem to be much of a consideration in the choice”, despite what a number of commentators have claimed.
Unfortunately, some, like William Saffire, continue to perpetuate these myths.
UPDATE: More here.