In Burning Wheel Gold, so far as I can tell, the following tests have open-ended die rolls:
- Any skill-based test with the funky little squiggly S after it (which are generally magic-based skills like elfsongs)
- Any skill-based test where the player decides to spend a Fate point to open the die rolls
Am I missing anything? I didn't think I was before, but I only recently came across Perception as being open-ended, so what do I know?