Let's talk about Rainbow Dash.
I think Rainbow Dash is one of the most interesting characters in My Little Pony: Friendship is Magic. I find her arc over the seasons to be the one that stands out the most to me, having noted it in several episodes, even ones where she isn't the focus.
When we're introduced to Rainbow, we get a good feeling for what kind of character she is: Brash, loud, and egotistical, but still having something of a good nature. She's a competitive pony who can't stand losing, and instead revels in boasting and showing off. The first interesting piece of depth for this character comes in "Sonic Rainboom", where we see that despite all that bravado, she's actually deeply insecure about failing to live up to her projected image. She's paralysed when it actually comes time to prove all of her boasts. Perhaps this comes from a fear that she can't actually live up to them, or perhaps the boasts are simply there to mask her insecurity. Regardless, she is ultimately put on the spot to save her friend, where she proves herself by performing a Sonic Rainboom, saving Rarity and the Wonderbolts who made to save her as well.
This early development is preceded by "Fall Weather Friends", where Rainbow's competitive streak has negative consequences. After tying for last place, Rainbow reflects on how her determination to win led to this situation. Specifically, she wound up focusing on one-upping Applejack instead of the race at hand, and as a result, the two were passed by all of the other contestants. We see this competitive streak come up again in "May the Best Pet Win!", where Rainbow creates a competition built to boost her ego. She places herself as a sort of ideal to be met, an illusion which is shattered when she's caught under a landslide. It's the tortoise, who simply wants to be given a chance, who stops by to save her. Touched by this act, Rainbow chooses to eschew the contest entirely, using a technicality to adopt the tortoise. Here we can see Rainbow starting to grow out of her previous attitude.
The turning point is, ultimately, "Read It or Weep", which is the final blow to Rainbow's insistence on her "cool" persona. After she find herself enjoying reading, her friends encourage her in her new hobby. With this support, she breaks out of her previous attitude and finds she doesn't have to worry about looking cool. This allows her to admit to having done "loads of nutty things" in "Dragon Quest", a sign of maturity. In "Hurricane Fluttershy", she makes herself talk calmly to Fluttershy and not get so aggressive, clearly having taken some of the lessons she and her friends learned to heart. To have Rainbow come from "Griffon the Brush Off" in season 1, where she didn't think twice about pranking Fluttershy, to being careful to speak to Fluttershy on her own terms is a very strong bit of character development. It shows Rainbow Dash thinking more about other ponies, and an increase in maturity.
This is best showcased in S3's "Wonderbolts Academy", where Rainbow decides that the titular Academy isn't worth the risk of harming her friends, even if it would help her achieve her dreams. This is in contrast to the aggressive techniques seen in "Fall Weather Friends", with Rainbow sticking to her guns and worrying about how her actions affect others. When Rainbow and Applejack compete again in "Castle Mane-ia", it's far less aggressive on Rainbow's part, and comes across as a much friendlier competition, largely on behalf of Rainbow not taking it too far. It's not the biggest example of her personal growth, but it does show how she's changed.
Rainbow starts out brash, arrogant, and a little self-absorbed, but grows to have a greater consideration for others, the ability to admit to her faults, and interests that she would have previously thought of as "uncool". She has come a long way since S1, and it shows, with one of the show's best character arcs-at least in my opinion.