To Split or to Not Split Infinitives

I have heard the rule that it is not acceptable to split an infinitive. I should write, “to act quickly,” and not, “to quickly act.” However, in college I was never taught this rule, and, furthermore, The Allyn & Bacon Guide to Writing (3rd ed.; eds. John D. Ramage, John C. Bean, and June Johnson; New York: Pearson, 2003) makes no mention of split infinitives. In fact, The Chicago Manual of Style (15th ed.; Chicago: University of Chicago, 2003) states that adverbs are acceptable for splitting the infinitive (§5.106) especially “to add emphasis or to produce a natural sound” (§5.160). While Grammar Girl acknowledges that it is acceptable to split an infinitive with an adverb, she advises not to split infinitives:

On the other hand, there’s also no reason to deliberately split infinitives when you know it’s going to upset people. The safer path is always to avoid splitting an infinitive. I would never split an infinitive in a pitch letter to an editor, for example, because there are certainly editors out there who believe the myth. If you want to get the assignment, don’t split infinitives. For the same reason, I’d never split an infinitive in a cover letter for a job.

More information about the history of avoiding split infinitives can be found at Wikipedia.

So, I leave it to you: should we split infinitives or not?