Anyways is a colloquial variant of the adverb anyway. It has a casual tone and may be considered out of place in formal or serious writing. In such contexts, anyway is safer.
Although considered informal, anyways is not wrong. In fact, there is much precedent in English for the adverbial -s suffix, which was common in Old and Middle English and survives today in words such as towards, once, always, and unawares. But while these words survive from a period of English in which the adverbial -s was common, anyways is a modern construction (though it is now several centuries old).
Anyways is sometimes useful for creating an informal or colloquial tone, which may be what these writers have in mind:
Anyways, it’s time to move on. [NY Times]
Whatever. Home Improvement sucked anyways. [Bleacher Report]
But in writing that is not intended to have a colloquial tone, anyway works in its place—for example:
Why is Google building a Google phone, anyway? [The Atlantic]
It can be nearly impossible to see from publicly available data which banks are extending or restructuring loans they believe will one day fail anyway. [Wall Street Journal]
Anyway, I think it’s pretty hard to make a bad Hurley episode. [Chicago Tribune]