Occasionally, I see people, even historians, use the term "barbarian" to describe various groups of people throughout history, commonly including but not limited to the Germanic Tribes, Gauls, Celts (in the context of Ancient Roman history), as well as the Huns, Mongols, and Xiongnu.
So I guess my question can be broken up into a couple of parts:
In any serious discussion of history, would it be proper to use the term "barbarian" to describe certain groups of people? Is there a value judgement implied in calling a particular group "barbarians?"
If so, what makes a group "barbarians?" Lack of urbanization? Technological disparity?
If not, what would be a better term to use? Stateless people? Or do we even need a term at all?
Your question is an important one and especially since you bring it up in terms of other groups that wouldn't have originally had that originally Greek term attached to them.
So, let's talk about the groups that you mention that fit more into my area. You have the groups you mention like the Xiongnu or Mongolians, but you also have many many more groups that can be grouped into, basically, "not chinese but groups that are around". Jurchen, Khitan, Tangut, Uighur, on and on and on. And there's quite the variety of terms that get used in textual accounts, depending on who's writing them when and who they're writing about. And a lot of times, you see the term "barbarian" thrown around in English translation. Is that useful? Somewhat, to get across the translation of an account that is reflecting a negative attitude towards some group, in a roughly comparable way to maybe how the Greek or English usage of the term would be used.
Now, should we be calling these groups "barbarians" in our context? Most likely not. What actual term we use is a little tricky, but to call the Mongolians, quite a diverse group even pre-Chingghis, "barbarians" is much less descriptive and far more simplified than saying something along the lines of "semi-nomadic peoples".
Your last point is one I don't have a great answer to. To me, it's much better to call the Jurchen the Jurchen and the Xiongnu the Xiongnu rather than group them under some fairly complex umbrella like "Northern Chinese semi-nomadic people" and so on.
EDIT: One thing you may also find interesting, is our recent Monday Methods feature on "tribe" as a grouping of peoples.
In a historical sense, I would say no. In a serious historical discussion, I would assume that most parties would already have a basic knowledge of the typical "barbarian" peoples (for my side of things I am sticking with the Western cultures), and it would be more appropriate to actually name them, thereby bypassing any confusion that might arise because of the extreme over generalization that might occur.
But you might also want to remember that when you talk about barbarians to a regular chap, he probably won't be thinking about the Celts, but about Conan. That's because the term has somewhat evolved into the "noble savage" trope, and it is a pretty important word used to describe different themes in literature. So even if it may not have historical value, it does still have some inherent use.