We have a lot of information about texts that were floating around in Greek antiquity which have since been lost, and most or all of them would presumably have had copies in the Alexandrian Mouseion. But if you're asking about texts that were lost for good when the library got burnt in 48/47 BCE, then the answer is "hardly any". It was the biggest library of its time; it certainly wasn't the only one.

Greek texts that survive intact today are probably not a representative sample of the texts that were available in the 1st century BCE, as conscious selection played an important role in their survival. However, the texts that survive contain many thousands of references, allusions, and quotations from lost works, and because of the sheer scale of the evidence it makes a bit more sense to treat that as, if not totally representative, then at least less unrepresentative. Just to give you a broad idea of what the make-up of these fragmentary works looks like, with the titles of the modern editions where the fragments are compiled:

• a few thousand historical and geographical authors (Jacoby's Fragmente der griechischen Historiker)
• about two hundred heroic and didactic epic poems from before 400 BCE (my own count; I haven't counted up the ones from after that date!)
• about eighty natural and ethical philosophers from before ca. 400 BCE (Diels & Kranz, Die Fragmente der Vorsokratiker)
• a bit over fifty lyric poets from before ca. 350 BCE (Page's Poetae melici graeci)
• a bit over 150 poets from ca. 400 BCE up to the Roman era (Lloyd-Jones, Supplementum hellenisticum)

And those are just the fragments that I tend to work with: it doesn't include fragments of grammarians, medical writers, mathematicians, astronomers, mythographers, religious tracts, and so on. Modern collections of those fragments exist too, but they're less centralised. Anyway, the natural inclination is to expect more of the same.

We'd also expect Greek translations of some non-Greek texts, and some of those would be very historically valuable: translations of astronomical and mathematical texts that had existed in the library of Ashurbanipal, for example; probably even some Egyptian texts (though that might be a stretch, and it's very hard to guess what kind of texts). These would be only a very, very tiny proportion of the collection, but it's quite possible that the Mouseion's copies of these may in some cases have been the last copies to survive.

A couple of older threads might provide some more food for thought:

• Is there a chance that before its destruction the library of Alexandria contained information that we still don't know today?
• How do we know which ancient books were lost?