Writers should avoid splitting an infinitive when?

Most of us were taught (if we were taught grammar at all) never to split infinitives, but writers have been splitting them anyway--even long before the creators of the Star Trek series provided us with the often-quoted phrase "to boldly go where no man has gone before." Those of us who were taught that the split infinitive is anathema might well benefit from examining the origins of this rule and considering cases where we might, with good reason, be excused for ignoring it.