Andy aka Jungledoc asked about this article on the EXRX forums, so I searched for it. I realized I'd never kept a link to it either, nor discussed it here.
The Thib System — Fatigue and Best Exercises - Basic Principles Behind My Updated Training Philosophy by Christian Thibaudeau
The article's look at when to train to failure is really valuable. Scroll down to "Principle #1: The Point of Fatigue Induction is Exercise Dependant" [sic - it should be dependent]
It has a chart outline what exercises work best taken to failure, and when to stop those that don't respond well.
This shouldn't be taken as true for all people in all situations. There are situations where you'll want to either avoid failure or induce failure, contrary to the chart's recommendations. But it's a very good starting point. And unless you know why you'll want to, say, take pullups to past-failure this session, you're better off cross-referencing on the chart and following those recommendations.