Baxter–Sagart seems to be the big one these days.
Are there any recordings of Old Chinese pronunciations available?
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I doubt it. Baxter and Sagart themselves mention, in their recent book on Old Chinese, that the reconstruction is at least partly schematic: The symbols are meant to be phonemic, not phonetic. Roughly speaking, that means that their main function is to trace the etymology of the spoken language, not to reflect how the sounds were actually realized. In many cases, they know no more about a particular sound than that it was a consonant of some sort, or sometimes that it was a velar consonant, or a guttural consonant, or some kind of lower vowel, or whatever. However, they have decided to use a convention that makes sense, that whenever a sound has so-and-so kind of reflex in the modern languages, or in Middle Chinese, then it will be represented with such-and-such a symbol in their Old Chinese transcription.
In reality, in most cases, the sound probably was something like what they transcribe, but not reliably so. At one point, a few years ago, Baxter and Sagart produced a "simplified" version of their reconstruction, which filtered out some of the uncertainties and made various specific decisions about which sounds went where. They decided in the end to scrap that version, because they felt it conveyed an unrealistic level of assuredness about the sounds of Old Chinese.
At any rate, even if one were to pick a particular realization of the phonemes of Old Chinese, it would probably take a lot of effort to learn to speak it fluently enough to read, say, Confucius, and no one is going to put in that much effort if there's a good chance a large percentage is just plain wrong.
In IPA, reconstructions are prefixed with an asterisk *, which is the linguists' reminder to the reader that the presented reconstruction isn't proposing that this is how people actually spoke, but an ancestral model which can explain the sounds of today.
Its purpose is only to help people draw etymological connections, not anything else.
This being said, some people have attempted to read OC reconstructions (上古漢語擬音) in coherent pieces of text, and you can find some samples on Youtube. For example, this video (up to 47s) is a rendition of Classic of Poetry's Startfruit Tree in the Marshlands (隰有萇楚) in Zhengzhang Shangfang's reconstruction (鄭張尚芳擬音):
*ljɯb ɢʷɯʔ daŋ sŋ̊ʰraʔ // qral naːl ɡɯ kje // qrow tjɯ qoːwɢ qoːwɢ // ŋraːwɢs ʔslɯʔ kje ma ʔle
*ljɯb ɢʷɯʔ daŋ sŋ̊ʰraʔː // qral naːl ɡɯ qʰʷra // qrow tjɯ qoːwɢ qoːwɢ // ŋraːwɢs ʔslɯʔ kje ma kraː
*ljɯb ɢʷɯʔ daŋ sŋ̊ʰraʔ // qral naːl ɡɯ ɦliɡ // qrow tjɯ qoːwɢ qoːwɢ // ŋraːwɢs ʔslɯʔ kje ma hlig