For example, Did Socrates really meet Zeno in Parmenides as a young man and the conversation that took place between them was recorded by Plato?
Are ANY of Plato's dialogues recordings of actual conversations?
Both of the answers are correct to point out that the dialogues are fictitious. It is extremely unlikely any section of any length is a transcript of an actual conversation between Socrates and anyone.
This, however, should not surprise us because the idea of making dialogue in a written work a transcript is a modern concept. No one would have done so until well past 1500 CE.
So in a sense, we need to split this into two parts. Cicero's speeches are also fictitious in that what we have recorded is not what he said but rather a highly polished version written well after the fact expressing what Cicero wanted to express. Same with Julius Caesar and most other classical Greek and Roman writing. But the ideas and thoughts contained therein are Cicero's or Julius Caesar's. (Aristotle's works by and large appear to be an exception -- not as in they are transcripts but as in they seem to be unpolished lecture notes). Let's call this feature "polishing your memoirs." This was and is common and doesn't strike me as wrong (Heidegger's later essays for instance are often papers he delivered several times and revised and improved along the way -- but that doesn't mean we would not say he was delivering the same paper).
A more important thing to notice is that Plato's Socrates often functions as a mouthpiece for Plato and does not necessarily say what Socrates would have said. In Plato scholarship, dialogues are divided into early, middle, and late. Early dialogues. My AOS is not Plato, but the basic gist is that early may be closer to what we believe Socrates himself might have done and said (i.e., someone who didn't claim to know things, asked questions about knowledge claims) and that late dialogues present Plato's elaborate theory of knowledge in sophisticated terms (probably not a view that Socrates held). (this is a key focus of Kierkegaard's dissertation The Concept of Irony and a returning theme in his writing). Let's call this "the Plato-washing of Socrates."
As far as I know Plato's dialogues are fictitious.
E.g., Parmenides died at about 460 BCE in the South of Italy, while Socrates was born at 470 BCE in Athens. Hence the meeting of Parmenides with a young Socrates, teaching Plato's theory of forms, cannot be historical.
Even when the dialogues are fictitious, some of the interlocutors in Plato's dialogues are historical, e.g., Aristophanes, Alkibiades, Agathon, Socrates in Plato's Symposion. But we do not know, whether such a meeting actually took place and whether the participants hold their speeches as recorded by Plato.
Usually Plato lets others express his own philosophical thoughts and claims, most notably Socrates. Plato's work with the highest probability for historical truth is the Apology, with the two speeches of Socrates.
As @JoWehler notes, the dialogues are fictitious compositions, though often with real people, including, I believe, two of Plato' brothers in the Republic.
Some passages from Socrates can be compared with Xenophon's works, but it is good to remember that what we possess is only a tiny fragment of ancient writings, and I think it would be very difficult for scholars to cross-reference works and judge accuracy.
Even the near-contemporary historians Herodotus and Thucydides, who ostensibly aimed for accuracy, are assumed to have partially fabricated public speeches they attribute to Pericles and other political leaders.
However, the period still bore many traces of oral culture. It is almost certain that the Greeks had far better memories for long speeches, poems, and dialogues than we do today. So it is possible that large chunks of dialogue were passed down with fewer errors than we might imagine.
G. M. A. Grube, in Five Dialogues by Plato, indicates that it's likely that the Apology, at least, is at least somewhat faithful to what Socrates actually said, given that Plato is believed to have written it not long after Socrates' trial, and it would have not gone over well had his account been drastically different from others' recollections of what Socrates had said.
It's worth noting that no less an authority than Plato's most famous pupil Aristotle classified his dialogs as "fiction." There's no conclusive way to prove the dialogs are all fictitious, but we should keep in mind the following two facts which are generally true:
Plato's aim was to teach philosophy, not record history (and he's on record as endorsing the alteration or wholesale invention of "facts" to suit philosophical or pedagogical goals).
Since Plato himself does not appear as a character in his own dialogs, we can assume he's not recording conversations where he was himself present. In order for them to be accurate, therefore, Socrates would have needed to have accurately recounted these conversations to Plato, who would then have also needed to remember them accurately for (in some cases) quite a long period of time before writing them down. This seems especially unlikely in light of Plato's aforementioned contempt for factual accuracy. Therefore, while Socrates likely would have had conversations with many of the people mentioned in the dialogues (since they tend to have been well-known figures of a certain social status in a fairly small community), the chances that those conversations were reproduced accurately are vanishingly small.
The most likely exceptions to this general rule are the trial (Apology) and death (Phaedo) of Socrates. In particular, the Apology was written relatively close to the time of the event it depicts, and Plato would almost certainly have personally been in attendance. It's also one of the few of Plato's Socratic works that depicts an event also attested to by independent observers. Judging by their accounts, Plato's version is neither entirely truthful nor entirely invented.
The Phaedo is generally considered to have been written later, and Plato explicitly mentions in the text that he was NOT present when it happened (which reads like a signal to readers to view it as fiction) so it's even less likely to be accurate. All the other dialogs are increasingly less likely to be non-fictional, for the reasons detailed above.