Is It Better To Never Split Infinitives?

Or is it better never to split infinitives? If you can't see any difference between the above two questions, you're probably right - as far as meaning goes, there is none.
Teachers always used to tell (or used to always tell) their pupils not to do it (or to not do it.) However, many witers have always split infinitives if they felt like it, on the grounds that the "no splitting" rule is based on Latin (which had distinct infinitive words )and is irrelevant to English because, actually, English has no infinitive.
The "mistake" (if you call it that) lies in putting an adverb between "to" and the main verb ("to boldly go...") because we regard "to go" as the infinitive form. But if you decide that "go" on its own is the infinitive (or base form) then there's nothing to split!
Most grammar experts now agree that it's better not to pointlessly split infinitives, but feel free to fearlessly do it if it will make the sentence stand out more.