Did Neville Longbottom ever know of his own importance?

Question

I have always found the prophecy story-arc through-out the Harry potter books to be especially intriguing. In some respects, I've always thought it was a "hat tip" to the conceptual butterfly effect^‡. A simple choice being the deciding factor between being the chosen one, or being (in poor Neville's case) one of life's "unlucky people".

I can't seem to recall if Neville ever becomes aware of his own importance, the significance that he and his family's fates played in the "chosen one" prophecy?

If he didn't know, then can we assume that J. K. Rowling orchestrated his important role and sense of defiance in the last "fight" (battle?) scene as a way of showing the reader (or viewer if you're watching the films) that Neville had the characteristics required to become the "chosen one" had fate played out differently?

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‡: Quoting from the relevant article on Wikipedia:

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The name, coined by Edward Lorenz for the effect which had been known long before, is derived from the metaphorical example of the details of a tornado (exact time of formation, exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier.

Answer 1

Nope.

To back up Voronwë's answer.

Neville's childhood had been blighted by Voldemort just as much as Harry's had, but Neville had no idea how close he had come to having Harry's destiny. The prophecy could have referred to either of them, yet, for his own inscrutable reasons, Voldemort had chosen to believe that Harry was the one meant.
_{(Half-Blood Prince, Chapter 7, The Slug Club).}

So, no, Harry never told Neville about the prophecy in the books. Of course, he could have shared it with Neville in later life but we have no evidence about this either way. My guess is that he wouldn't have put that burden on Neville, especially since the war had already ended by that point.

Out-of-universe answer:

In reference to why Rowling gave Neville the role that she did in the final book, the only comment I've found where she's really addressed that scene is here:

Su: How did Neville get the Gryfindor sword? Is there a link to the hat?

J.K. Rowling: Yes, there is very definitely a link to the hat!

Neville, [a] most worthy Gryffindor, asked for help just as Harry did in the Chamber of Secrets, and Gryffindor’s sword was transported into Gryffindor’s old hat – the Sorting Hat was Gryffindor’s initially, as you know.

Griphook was wrong – Gryffindor did not ‘steal’ the sword, not unless you are a goblin fanatic and believe that all goblin-made objects really belong to the maker.

So, apart from saying that Neville was a "worthy Gryffindor", Rowling doesn't really say why Neville was the one she chose to kill Nagini. I don't think it had anything to do with the prophecy, though - even on a literary level. Personally, I think it's just the case that Neville was a major character who was around at the time. And he had the bravery and temerity to do the deed, which other characters wouldn't necessarily have had. Nevertheless, there was no fate involved in Neville killing Nagini. It was just a badass moment for his character, pure and simple.

Answer 2

No, because the full prophecy wasn't exactly known to the general public.

“Who heard it?” asked Harry, though he thought he knew the answer already.

“I did,” said Dumbledore.

Except for Dumbledore and the Keeper of the Hall of Prophecy (later Harry, Ron and Hermione), no one knew of the prophecy's (full) content. Both Snape and Voldemort heard the part about:

“He heard only the first part, the part foretelling the birth of a boy in July to parents who had thrice defied Voldemort.

Dumbledore only told Harry, who only told Ron and Hermione. We don't know if Snape and Voldemort relayed this information to the Death Eaters, but even if they did, they didn't seem to bother reminding Neville about it in the Battle of the Department of Mysteries.

Harry’s heart began to race. He had not told Ron, Hermione, or anyone else what the prophecy had contained. Neville had told them it had smashed while Harry was pulling him up the steps in the Death Room, and Harry had not yet corrected this impression. He was not ready to see their expressions when he told them that he must be either murderer or victim, there was no other way. . .

Therefore, unless Harry told Neville about the prophecy after the Battle of Hogwarts, Neville had no idea that he was so close to becoming the Boy Who Lived, instead of the Boy Who Keeps Losing His Toad.