Very, very, very many. Enough that making available information about lost works more comprehensible and accessible is always an extremely important form of research. An enormous amount of historically valuable information can be gleaned from making inferences about the relationships between sources used by surviving writers. (That information sometimes takes the form of deducing that a surviving source is wholly untrustworthy! -- e.g. any of Plutarch's writings about anyone who lived before 400 BCE or so.)

In the area of Greco-Roman antiquity, this takes the form of large ongoing projects like Brill's New Jacoby, which is an updated and improved form of Jacoby's Fragmente der griechischen Historiker (and which has recently released a large update!) or the British Fragments of the Roman Historians project. We know varying amounts about a couple of thousand lost Greek historical writings: just the fact that a work existed in some cases, an enormous amount of detail in others. If you have access from a university campus, try this collection of fragments of one of the most important lost Greek historians. Roman historians are much more poorly represented, but we have some information about a few dozen lost Roman historical writers.

Similar comments apply to lost writers in other genres, though the number of lost works tends to be lower outside the field of history. The edition of fragments of the pre-Socratic philosophers by Diels and Kranz includes fragments of about a hundred lost philosophers. I recently compiled a list of lost Greek epics earlier than 400 BCE, and found that we know about ca. two hundred of them. There are several collections of the fragments of other lost Greek poetry; one like Lloyd-Jones' Supplementum Hellenisticum includes fragments of nearly two hundred poets of the fourth to second centuries BCE.

Quite a few. For instance, we're missing some big chunks of Livy's history of Rome. IIRC only volumes 1-10 of about 150 are complete, with the others being fragmentary.

Ancient Egypt is another big one. We have lots of fragmentary references to things, but few actual complete texts. We do not, that I recall, actually have a complete copy of the famous Osiris drama (Osiris fights with his brother Set, Set chops him up, Isis brings him back, etc.,) but rather we've assembled the text from several incomplete sources.

In summary, there's a lot of stuff which ancient historians refer to (or which we can guess at by its absence in their texts,) which they probably simply assumed we would know.

For examples, look up Livy's "Ab urbe condita," and the writings of Tacitus and Polybius.

For Egypt, look up the Heqanakht papyrus.