Since a great many human languages have not been recorded in any way, I'd have to say no. There is a popular book by Peter Ladefoged and Ian Maddieson called the Sounds of the World's Languages that goes a long way to describe all the sounds we know of.

I think this guy God did one time.

He called the inventory OM.

AUM.

I E A O U M.

eeeee ehhhhh aaaaaa oooooo uuuuuu mmmmm.

:)

This is not as simple a question as it sounds. Well, first of all, the question itself is ambiguous -- "comprehensive inventory" sounds like you mean all sounds that occur anywhere, whereas "common to ALL human languages" sounds like you mean those sounds that occur in every known language.

In order to address the questions, but especially the first one, you would have to take into account the difference between phones and phonemes. Counting the number of phones (sounds) in languages, including all their dialects, would be like counting the number of fractions between 1 and 2. Phonemes, OTOH, are like the boundaries that a language draws between sounds. For example, the queen of England's pronounciation of the vowel sound in "know," the way an Australian does and the way I do would all be different phones. But those sounds are a single phoneme in English, because all English speakers would regard these sounds as variations of the same vowel. The vowel sounds in feet and fit can both be found in Spanish, but in Spanish they are a single phoneme; a Spanish speaker would regard those as variations of the same vowel sound. The test is that switching between one and the other would not cause a word's meaning to change. But in English, those are separate phonemes; sin and seen are distinct words. An English speaker is likely to consider the initial sounds of call and kill as the same phoneme, but an Arabic or Quechua speaker would hear them as distinct sounds. And so on.

Some languages of the Caucasus divide the voiceless velar fricative (German ch sound) into five different phonemes, depending on how far back in the mouth it is pronounced. But as you can guess, there are potentially unlimited potential fine divisions that could be made in that one sound, even though there are practical limits on the fineness of phonemic divisions humans can handle in their language.

But for practical purposes, if you can find a complete version of the IPA, it can give a general idea of the phonetic range of human languages, including things like tones, clicks and plosives.

Now, if your question is about what sounds are common to all human languages -- the Hawaiian language has the smallest phonemic inventory known, so let's look at that. Subtract the glottal stop, first of all, which is not found phonemically in English (or any European language, to my knowledge). Are the rest of the sounds are common to nearly all languages? Well, l/r is lacking in some, so subtract that. One would think that m would be universal, but the Iroquoian languages lack labials, so that gets rid of m, and p too. Tahitian lacks a velar stop (k sound) and a sibilant (s/sh/z/zh). What are we left with. Maybe n and t are common to all languages in some form. Maybe not. I don't know any language with fewer than three vowel phonemes (a/i/u). But there may be some.

it'd be really neat if there were an online inventory with audio samples of many of the phonemes...especially the ones that are more unusual vis-à-vis English...

There is a CD for called "sounds of the IPA"

www.phon.ucl.ac.uk/shop/soundsipa.php

They have lots of other products as well.