Is it ever appropriate to address a fellow Service Member by last name alone?

I think in basic we all went through that but once you've had your brain altered and reprogrammed it should be rank and last name under most situations. I occasionally slipped and called soldiers E-4 and below by last names but corrected myself because it doesn't show the same respect that we ask for in return.

There is a time and place for everything. I think it is appropriate if that kind of relationship has been established.

When I was in our division mixed it up. Our division officer was Sir, ASWO, or Ens (later Lt.) Williams. If we were not just amongst our division it was always Sir. Our Chief was always just addressed as Chief, unless there were other chiefs present, then it was Chief Simmons. Petty Officer were addressed by their last name, or STG1,2, or 3 accordingly. It was never meant in a disrespectful manner, it was simply a culture of bonding that was encouraged. Hell I have a hat that says Big Pappa Spank because there were those who were convinced I would end up as a WWE wrestler of that name. 
If it was a person from outside of our division, it was always their proper title. CO was always Captain as that is the title he earned as commanding officer of a ship. 
Funny thing is that my step kids address me as "Sir"

It depends on the rank and who it is coming from. I would've rather had been called Sgt but my closest friends or fellow NCO's used to just call me V. Especially down range. Very informal attached to SF and I absolutely LOVED IT!

I see that if a peer of superior does it as fine. Most people don't like saying it twice! LOL

When u are addressing someone with a higher rank than yourself it is proper military custom and courtesy to use the rank when addressing them. This is just common sense but it does elude people from time to time and its just a simple on the spot correction and hope it sticks with them.

Good question, Burns, good question...

I picked "This is only appropriate coming from a peer or supervisor. " however, I would like to say I always adressed Soldiers by their rank that they earned. It should give them more pride in what they are and what they earned.

Depends on your unit, but with a last name that you can't help but annunciate a certain way - Van Ass(e) - I was fine with those above me calling me by last name only. Sgt. VanAss(e) to the younger airmen...

My BDE CSM called me Mike and I called him Sergeant Major. I am not a big fan of superiors calling juniors by their first name. I know the officers do it on a regular basis but as NCOs I don't think it sets the proper example.

Among peers I have no issues unless there are junior Soldiers around, then rank should be used.