Ron is, surprisingly, left out of a hugely important part of Harry Potter and the Prisoner of Azkaban, as he doesn't go back in time with Harry and Hermione in the end. Throughout this installment of the Harry Potter series, in fact, Ron tends to be very much on the side, with the focus of his story seeming to be his attempts to protect Scabbers, and blame Hermione for Crookshanks' hatred of the 'rat'.
However, Ron does make a few particularly good decisions in the end - even if only one of them has a real impact on the future of the franchise. Despite this, his decisions throughout The Prisoner of Azkaban show some real growth, and some loyalty - which is often his defining characteristic in Harry Potter.
Sending Harry A Sneakoscope
Although this doesn't end up having a huge impact on the story, it was actually a good choice of Ron's to send Harry a Sneakoscope as a gift after his trip to Egypt. Harry, unfortunately, assumes that it is broken when it keeps going off, and buries it in his trunk, wrapped in a sock. However, this is a useful Dark Detector which is a great gift for him!
Sadly, this doesn't end up having a particularly big impact over the rest of the series, but it certainly could have done - and had Harry paid a little more attention, he may have figured out there was a problem a little bit sooner! No matter the eventual impact though, the gift was still well-chosen.
Trying To Defend Harry
When Malfoy sees Harry in Hogsmeade and runs to report him to Snape, Harry has to race to get back before he is found missing. And when Snape asks him to turn out his pockets, it seems like he may be in trouble anyway... because they are filled with sweets from Hogsmeade! Ron, however, races back to the castle himself to burst upon Harry and the Professor, claiming that the sweets (and Marauders Map) are from him, and that Harry didn't do it!
Of course, absolutely no one believes Ron - Snape clearly knows that he is lying, as does Lupin (thanks to knowing what the Marauder's Map is), but Ron's well-intentioned choice is still a good one. It proves to Harry how loyal he is (as if there was any doubt!), but it also allows Lupin to pretend that he believes Harry, and to dismiss Snape - who may have otherwise doled out a punishment!
Helping Hermione Try And Defend Buckbeak
Although this is a story arc that is a much bigger focus in the books than the movies, Ron does try and help Hermione (and Hagrid) with Buckbeak's defense - something that is eventually unsuccessful, but still very well-intentioned. Given how much Ron absolutely hates studying, too, this is a pretty big deal for him!
They don't manage to win the case, but what they do manage is to strengthen their relationship - not just the friendship between Ron and Hermione, but also between Ron and Hagrid. Especially given how hard Ron is on Hermione over the course of this school year, making the effort to do something that he hates so much to help her with it is a big deal - and a great decision.
Patching Things Up With Hermione
Hand in hand with helping Hermione work on Buckbeak's defense, Ron's decision to actually fix his friendship with Hermione is one of his most impactful decisions in The Prisoner of Azkaban. He is furious with her for so long because of Crookshanks and Scabbers, and it actually takes prompting from Hagrid to sort things out - but if he had not decided to, things would have been truly ruined!
The friendship between Harry, Ron, and Hermione is what truly saves the Wizarding World, as none of them could have defeated Voldemort on their own - so had Ron not made the effort to repair it at this point, it would have been a major issue! They may not even have got to that point in the series, either, as it is Hermione's involvement in the final scenes of this book that saves all three of the Golden Trio (not to mention Sirius and Buckbeak).
Running After Scabbers
In many ways, this was a foolhardy decision - the choice to dive after a pet rat, when it means running toward a suspicious, dangerous-looking, giant dog, is not a smart one! Given that this also meant running straight toward the Whomping Willow - which Ron and Harry know well as dangerous - would make this seem like a completely ridiculous choice.
However, in the end, Harry Potter fans know that had Ron not done this, everything would have been different. Had Ron left Scabbers to run away, Sirius would have got hold of him, killed him instantly, and spent the rest of his life on the run - with no one knowing that he was innocent all along. Instead, Ron's seemingly dangerous decision led to the truth coming out, and Harry and Lupin realizing the truth.