There are a ton of ancient Greek and Latin texts that would be highly valued today, if they had survived, but their loss was not necessarily because of mishaps at Alexandria. Most lost ancient texts are lost via a long and complicated process over many centuries, and are the combination of accident and disinterest even in the ancient world. Here are a few less obvious examples:

Anaxagoras of Clazomenai, one of the earliest pre-Socratics. He was notorious at Athens in the late 5th century and influenced Socrates, Plato, and Aristotle (among many others). If his single work on philosophy had survived, it would surely be an often-read and cited text in college philosophy courses. There are many many more "wish-we-hads" in the realm of philosophy.

Aristotle's (probably) lost second section of Poetics, focused on Greek Comedy. As someone who has worked with Aristophanes a lot, this is probably the one lost bit I would want returned the most.

Cato the Elder's Origines, which detailed the early history of Rome's rise and relations with the Italian states. This work was, of course, very moralistic and pro-Roman, but also detailed the larger Italian towns and their foundation myths. There was a lot of mythological and quasi-mythological detail of Italy there which has been largely lost. A good number of fragments exist of this work, from which we can get an idea of what it was like (and it seems awesome).

The emperor Claudius was a bit of a history buff, and wrote several interesting works, all now lost. He created a dictionary of Etruscan words, and also wrote an Etruscan history. Modern Etruscan scholars would probably murder their mothers to get a look at either of them. He also wrote a pretty detailed account of Augustus' reign, and a book of Carthaginian history (which seems, alas, to have been bargain bin calibre). Still, he had privileged access to a lot of obscure, cast-aside sources and had an army of scribae to help him with his literary pursuits. I don't know much about the history of how and why his works were lost, but I'd be interested to learn more.

Agatharchos of Knidos wrote several histories, including an "Affairs of Europe" in 49 books. None of it survives, but other stuff of his does survive and seems very competent. For whatever reason, he was not well-respected in the ancient world. His history would probably give us some key new historic insight, especially for the doings of Alexander and the Hellenistic period following. We have part of his description of the Red Sea, and it is pretty great. He seems very adept at incorporating a lot of disparate sources into a coherent whole -- in other words, a good historian.

Callisthenes of Olynthos wrote several works, all lost, one of which was an account of Alexander's campaign. Sources for this are really lousy, so that would be nice to have, even though Polybios consulted it and complained about bad it was.

Suetonius (the Roman biographer of the first twelve emperors) wrote a metric ton of crazy stuff, none of which survives. In particular, he made a collection of Greek insults which was probably amazing and very thorough. He also wrote a collection of pseudo-biographies of famous whores. More seriously, he wrote a monograph on "Cicero's Republic" which might have been interesting, and also an enigmatic work which seemed to deal with the process of editing a literary manuscript. And many others I won't list.

Pherecydes was a mythographer who wrote a ten-book collection of genealogies of gods and heroes. He's not as famous as some other mythographers, but a lot of his work survives in fragments and is the basis for our knowledge of the more obscure Greek mythology. A lot of times we have to fall back on Ovid for details of some obscure myths, and if Pherecydes' work had survived we would surely be in better shape there. We certainly don't NEED this, and we have plenty of myths to talk about, but it would be nice to have.

A lot of Lucan's works are lost, but I'm not particularly sad about that (sorry Silver Age fans!). You can get your fill of Lucan in his work Pharsalia.

HOMER'S MARGITES. It probably wasn't written by "Homer," but whatever -- this was a comedy-epic about a regular joe, a guy who was NOT a hero. Aristotle records a few lines from it, from which we learn that the main character Margites was "good at nothing." He was dumb and had a lot of sex. Truly a tragic loss for civilization.

Finally, personally I would love to have Sulla's memoirs, but there are probably more important lost works to recover first. Caesar's letters would also be nice to have -- we have a few preserved in Cicero's dossier of letters, but I want more! And maybe some more from Pompey.

There are hundreds more examples.

An important point to address is that it isn't entirely clear when (or if) the Royal Library of the Ptolemeic Dynasty was actually burned. It was certainly somehow destroyed or dissolved over many centuries, but it isn't clear that there was one event, the way this is often discussed. As ubiquitous a reference point as this event has become, there are a lot of questions about the history and a lot of conflicting information from ancient writers. Various culprits have been proposed (Julius Caesar, Aurelian, the Christians, the Muslims), and this is covered in much more extensive detail here in a question asked by /u/alexandriaintrigued and answered by a user who has delted their account (this comment is still listed in the FAQ section of the sub, so hopefully linking it is alright).

In terms of lost works from the ancient world by famous authors... there are many. Significant portions of the works of well-known writers like Aristotle, Sappho, Pindar, Cicero, Sophocles, Aeschylus, Callimachus, Euripides, have not survived (or have not yet been found... this does happen, see below). Euripides, for example, wrote ~90 plays. 18 have survived in full, with fragments of others. Sophocles produced 123, of which 7 survive. Some prominent examples of highly-regarded authors with works that are entirely lost or known only from scant fragments would be the playwright Agathon (famed in classical Athens), the philosopher Heraclitus ("no man dips his foot in the same river twice"; "everything flows"), and the philosopher and mathematician Pythagoras (he of theorem fame); there are many more. (Edit: /u/Alkibiades415 just posted a much more extensive list above)

That depressing information being said, a bright spot is that "lost" works are sometimes rediscovered in libraries, dusty rooms in monestaries, and archaeological digs. A list of some "recently" rediscovered manuscripts can be found here. This site also has links to a good deal of scholarship on the subject of recovering lost manuscripts.