AC may or may not be required, based on three items:
1) local code - check with your local government
2) exposure to physical damage - if the cable is exposed to physical damage, then it must be protected by either AC or conduit. Your local inspector can provide input on what constitutes "exposure".
3) furnace manufacturer requirements - Whatever the manufacturer says must be obeyed.

Since all of your circuits aren't installed with AC, there's probably no local code that requires it. It's also fairly unlikely that the vent for a powder room would need to be protected unless the cable is exposed to damage. My best guess is that for some reason, the original installer believed that there was some exposure to damage, and decided to install AC. It also might have been installed for simple convenience to the installer...perhaps that's what he had "on the truck".

NM was not allowed for many years in houses over 2 stories above grade (might have been 3).

That rule was relaxed many years ago.

There may be local rules requiring AC, but NM is standard for residential work except in a very few places (Chicago requires everything in conduit).

Following on brickeyee, certain munnies have building codes that exceed the NEC code. As I have stated before, Dallas building codes require all hard wired smoke alarms to be on a dedicated circuit. Also, regarding kurto's remark, we follow code, not what we have on our truck.

To the OP, it may have been local code at the time for the applications in question. Why is it of concern to you?

On two widely spaced occasions my heater, which has a clock thermostat, has failed to turn on and warm up the house when the morning cycle came into play, around 6:30 AM. The dedicated funace circuit breaker had tripped. It is one of the 14/2 10 amps. When I call in an electrician to look it over with my luck he won't be able to duplicate the problem. I'm assuming he will want to rewire from the furnace to the circuit breaker panel. I would rather fish the wire myself and have him hook it up and save a few bucks in the process. Needless to say fishing regular cable is way easier than the armored stuff. If the latter must be used I'd let him do it. That's the reason for my original question.

Here's another: does 14/2 and a 10 amp breaker seem a bit light for a furnace? Wouldn't 12/2 and a 20 amp be more appropriate?

"does 14/2 and a 10 amp breaker seem a bit light for a furnace?"

#14 is good for 15 amps.

I have not seen a 10 A breaker in years except the push button type that are part of equipment.

A very careful checkout is probably in order.
What kind of furnace?

If it is forced hot air you may have a blower motor not starting up from wither a bad capacitor or start winding.

Pumped hot water can have the same problem with a circulating pump.

Brickeyee - I meant 14/2 & 15 amps not 10. Sorry for the brain cramp! Thanks for your input.

BTW it is gas w/forced hot air.

"BTW it is gas w/forced hot air."

I would check the start up current draw of the blower and note how long it is taking to come up to speed.

That is the largest load in a gas forced hot air furnace.

You can also turn it off, and see how easily the blower and motor turn by hand.

If shaft oil caps are present on the motor and/or blower some oil might be worthwhile.

If shaft oil caps are present on the motor and/or blower some oil might be worthwhile.

Years ago my furnace blower motor started making a horrible screeching noise. Of course, it was at 5 p.m. on a Sunday. No oil ports but I pulled off the end caps and put some oil on the cottony material that I presume was designed to act as a reservoir. Put everything back together and the sound went way.

Monday morning I ordered a new blower motor. Two years later when I sold the house the new motor was still sitting on the garage shelf. I figured if I returned it the old motor would fail at the most inopportune time. :-)