Many grammar books and online resources state that the rule of split infinitives is not a steadfast rule, and it is often broken by authors. Most English speakers break this rule routinely in speech, and it's largely accepted, even in written from. I agree with those who think it is an inappropriate imposition on English from Latin grammar rules.
Still, in some formal writing situations, I think it's best to avoid splitting an infinitive. But because it occurs so frequently, phrasing to avoid a split infinitive can make a sentence sound stuffy or as if it had a different meaning. For example, here is a sentence with an infinitive that is split by the adverb finally: "Mike was impatient to finally get his driver's license." There are several ways to rewrite the sentence following the rule:
Mike was impatient finally to get his diver's license.
Mike was finally impatient to get his driver's license.
Mike was impatient to get his driver's license finally.
While these examples are technically correct, the sentence structure is awkward and difficult to read.