High-energy physics. Yes, literally every paper that's worth your time is on arxiv first. The only time anyone reads from an actual peer-reviewed journal is when something that was on arxiv eventually gets published (you know, a year later) and might have minor corrections. And I don't know a single person that picks up journals for those crucial papers that were never posted to arxiv.
What's the point of "formal peer-review", anyway? If you're in the community you talk to your colleagues about what's on arxiv and you know what's good and what isn't. You don't need a journal to tell you.
For the areas I used to work in for many years, high energy physics and quantum gravity, I can't think of a single exception.
Of course I don't have total knowledge of these fields, only my corner of them, and I'm sure you'll find a counterexample if you dig deep enough, but if counterexamples are remarkable and rare, then the heuristic: "Not on the arxiv, not likely to be credible" stands.
>There are vast areas of research where every credible paper gets posted to the arxiv
due to your word "every" which from context you mean literally; no exceptions. So, what would these vast areas of research be? The statement would not be true for any areas of research I know about.
EDIT: Thanks for the replies - fascinating. That in certain fields, no paper is worth reading if not on arxiv.