I was taught that the closest analogue in English of Chinese measure words are 'units', e.g. "a pile of wood", "a cup of water", etc.
What strikes me as a bit odd about this analogy is that the units in English add semantic meaning to the sentence (see paragraph below), whereas in Chinese, it seems it is just some formal 'rule'. I find this particularly weird because Chinese isn't exactly a language with a lot of unnecessary morphemes floating about. It seems more Chinese to me to say “一男人” as opposed to “一个男人”; the “个” doesn't really add anything to that sentence, so, in the spirit of Chinese, I feel as if we should drop it.
Of course, all this would be explained if it did in fact add meaning to the sentence. In English, for example, we can say "a pile of wood", but we can also say "a stack of wood". In both cases, we have three things: the thing, the unit, and how many units, and the difference between the two is precisely the type of unit. I've been taught, however, that in Chinese, every noun has one and only one correct measure word associated to it, and in particular, you can't make the analogous distinction between the two cases in Chinese. Is that in fact incorrect, so that, in certain cases, more than one measure word makes sense for a particular noun? For example, can I say both “一瓶酒” and “一碗酒”? If it is correct, and one and only one measure word is correct for a given noun, why do they exist in the language at all (for reasons other than "It's just a rule.")?