There doesn't seem to be mention of other instances of public narration of their adventures, but some of the details were known anyway.
While Dumbledore only told Harry about the Horcruxes, and Harry only told Ron and Hermione, Harry did publicly reference them in his final duel with Voldemort:
"There are no more Horcruxes. It's just you and me. Neither can live while the other survives, and one of us is about to leave for good."
While it's likely that most of the crowd would not have known what Horcruxes are, or would have been too distracted by the context to understand what Harry was saying, there would surely have been some people who could have surmised what was going on.
When it comes to the prophecy, Dumbledore assured Harry in the beginning of Half-Blood Prince that they are the only two people who have heard its full contents:
"There are only two people in the whole world who know the full contents of the prophecy made about you and Lord Voldemort, and they are both standing in this smelly, spidery broom shed.
However, the public was able to more or less guess about the prophecy, as Dumbledore himself confirmed in his very next words:
It is true, however, that many have guessed, correctly, that Voldemort sent his Death Eaters to steal a prophecy, and that the prophecy concerned you.
And, of course, throughout the remainder of the series there are constant references to Harry possibly being the Chosen One, whether it be Daily Prophet articles, whispers in the Hogwarts corridors, Slughorn bringing it up at his party on the train, etc.
The events in the Ministry of Magic at the end of Order of the Phoenix surrounding the prophecy were reported in the Daily Prophet:
Details of the events that led to the Ministry turnaround are still hazy, though it is believed that He-Who-Must-Not-Be-Named and a select band of followers (known as Death Eaters) gained entry to the Ministry of Magic itself on Thursday evening.
The events in the Chamber of Secrets were narrated to an office filled with Dumbledore, McGonagall, and Mr. and Mrs. Weasley:
Then he started telling them everything. For nearly a quarter of an hour he spoke into the rapt silence: He told them about hearing the disembodied voice, how Hermione had finally realized that he was hearing a basilisk in the pipes; how he and Ron had followed the spiders into the forest, that Aragog had told them where the last victim of the basilisk had died; how he had guessed that Moaning Myrtle had been the victim, and that the entrance to the Chamber of Secrets might be in her bathroom....
While theoretically no one else should have known what happened, we find in Order of the Phoenix that at least some rumors had spread:
"And did you kill a basilisk with that sword in Dumbledore’s office?” demanded Terry Boot. “That’s what one of the portraits on the wall told me when I was in there last year..."
While Terry specifically mentions that a portrait told him, it is possible that the portrait told other people as well, or that rumors had spread some other way. As Dumbledore so eloquently said at the end of Philosopher's Stone:
What happened down in the dungeons between you and Professor Quirrel is a complete secret, so, naturally, the whole school knows.
In other words, spectacular events at Hogwarts tend to get publicized somehow.