Not long ago I published a rambling miscellany post in which I advocated the use of singular "they". Now, independently, there are posts springing up on the same same subject. Wolfangel has this argument post, followed by a post with examples from Shakespeare, C. S. Lewis, and Austen, and a link to the Austen page I had indicated. Wolfangel suggests in the former that the generic 'he' is actually vanishing; the younger generation has difficulty recognizing 'he' as ever generic. Then Sharon at Early Modern Notes published this post, in which she advocates all-out revolution. And All Day Permanent Red adds this post. So it begins!
I'm not convinced by arguments that 'he' never really functions generically, because (if nothing else) it does so by fiat, and in language that suffices; but I think the arguments put forward toward this conclusion all show conclusively that the generic 'he' runs into serious problems because of the existence of the masculine 'he' - it is very easy to build cases in which a generic 'he' would be confusing at best and (in general) leads to inconsistency. Maintaining 'he' as the generic pronoun is simply an unreasonable position when there is already a much better alternative in play.
Update: There are two other discussions of the subject over the previous several days here and here.
Update: As Rebecca notes in the comments, Parableman has a discussion of this issue, tailored to a particular topic, here.