What language did the ancient Minoans of Crete speak? Was ancient Greek, or something very different?

Other respondents have answered about Linear A, of which we know only that is probably inspired Linear B, and it was very unlikely to have been Greek.

We also have a few inscriptions, from Classical times, in Eteocretan language, a non-Greek language written in Greek characters. It’s reasonable to assume it’s the same language was what the Minoans spoke, though it’s not definite.

We only know two words from what little parallel Greek–Eteocretan text we have, and we know that it doesn’t look like any language we know from the region, including Semitic or Indo-European. We also know that it had syllabic consonants: lmo is a word in Eteocretan.

(From Praisos 2)