We've had this discussion before. The answer about appropriateness lies completely in the circumstances. If it is a rural or generally low-call volume department, with appropriate facilities for crew to sleep, work, etc, then I have no problem with longer shifts 12, 24, 36 hours, whatever. Oh yeah, and "on call" systems dont count-- that is systems that allow you to maintain your daily routine as long as you stay within the response area and appropriate transportation.
Now, systems with upwards of 8, 10, 12 calls/8 hours have NO place on shifts any longer then 16 hours. I dont care if those are emergencies, transfers, etc. At that point, the crew should no longer be driving, responsible for patient care, etc.
I will note that the company that I work for does maintain 2 ALS trucks on 24 hour shifts, and they may have a high call volume during the day, but they then have very few or no calls during the night and appropriate accommodations for sleep.
I am also a part of a college EMS corps. We also maintain 24 hour shifts "on call", but allow our on-call members to maintain their daily activities, sleep in their dorm, go to class, etc, as long as they stay on campus. We also average ~1 call/shift. I am in the middle of a ~3 day shift right now, but dont mind...