After being shot down at the end of Sky Chase Act 1, Sonic crash lands back in Station Square and the very first thing he does is worry himself sick over Tails, who was piloting the very same Tornado plane that got blasted down by Robotnik's Egg Carrier. Sonic really does care that much about his best pal.
After being sent by Eggman to interogate Amy for the bird she is protecting, she begs for Gamma to save it. After some hesitation (which upon he is shown to be physically pained by his emotional conflict), Gamma breaks open their cell and orders them to leave. He hangs his head dumbfounded and guilt ridden at disobeying an order (and being well aware of the penalty for disappointing Eggman by this point). Amy, feeling sorry for him, offers her friendship. The heartwrenching "Theme Of E-102" playing in the background only makes it more powerful.
In Gamma's story, she pleads with him to stop, not Sonic. All Amy has to do is say she knows Gamma isn't evil, and asks if he remembers her. After a second, Gamma lowers his gun.
Even more heartwarming in the less Narm-y Japanese version:
Amy: Mr Robot, you're not that kind of person, are you? Right? Please stop...
*Gamma pauses and lowers his gun*
Sonic:*dumbfounded* Amy?...I guess you have your reasons...
A case of Fridge Heartwarming: as Amy and Tails escape the plummeting Egg Carrier, Amy calls out to Gamma, saying that she hopes to meet him again. At the end of her story, she succeeds in reuniting Birdie with its family which includes the pink Flicky that was inside Gamma. So, in a way, Gamma and Amy did meet again.
Near the end in Knuckles' story, after he watches Sonic chase after Eggman, Knuckles states that he'll let Sonic handle things here and assures that he'll do okay, citing the respect he has for the hedgehog.
The ending also makes clear Froggy running from Big really was out of character. The thing follows it's master everywhere and jumps excitedly as they fool around, making clear it is as loyal to Big as vice versa.
Just the thought that EVERYTHING Big is doing through this game, up to and including fighting THE GOD OF DESTRUCTION is all in the name of reuniting with his friend is really incredible and goes to show just what kindof personBig is.
The ending of Tails' story when he decides to stop Eggman from destroying Station Square by himself, complete with townspeople cheering him on.
The entire ending of E-102 Gamma is both this and a Tear Jerker. After a climatic battle between E-101 Beta MK II, he finds that it was powered by a Flicky and as he walks past it, he realizes that he was the sibling of the Flicky inside E-101 and the birdie that Amy was taking care of. With this knowledge, Gamma succumbs to the damage he received from the battle and explodes, freeing the Flicky and letting all three reunite.
A small one for Sonic. In the last story, instead of simply resorting to sealing Perfect Chaos back in the Master Emerald, he'd rather find another way of putting a stop to him - by wanting to help the creature heal on the inside, help remove the anger the creature has harbored over the centuries.
And after Chaos is back to normal, Tikal soothes his mind by showing him that his precious Chao are living peacefully alongside humans, before the two of them ascend into the sky, finally at peace.
The Chao Gardens, full stop. They're a peaceful sidequest in which you're able to raise and bond with a variety of Chao with all six characters, and watch as they grow and play with each other.
A Chao that has bonded with a certain character highly enough will run to them in glee when they whistle, or occasionally skip over to them begging to be cuddled. Pick them up, and they'll often squirm with delight.
If you leave Sonic idle inside a Chao Garden, he'll say something along the lines of, "Are you guys being good?" In the same tone of voice a father would use to his children after returning home from work. D'awww.
Also in the Chao Gardens, watch after a Chao long enough as a certain character and when idle long enough, they'll draw an affectionate scribble of them on the floor should they be given the animal that bestows that skill. They'll even draw a chibi Gamma.
While Chao have a limited lifespan, should their happiness be high enough when they die they will reincarnate into an egg and hatch again, still with their memories, skills and being friendly as ever.
The very soundtrack itself has several of these moments since it's so expansive and variegated for a video game, let alone one in which you'll only hear a small section of most of the tracks. It really succeeds in conveying Sonic's character; a speed demon with a love of adventure and soaking in the splendor of his surroundings without a care in the world (it's what he even says in his theme song, It Doesn't Matter). Choice moments that just cry out The World Is Just Awesome include the introspective piano solo of the faster second Emerald Coast track, the "At Dawn" track which concludes Speed Highway, and the aforementioned It Doesn't Matter appearing in the Twinkle Circuit track.
A small one, but when Eggman states his pride in Gamma for finding Froggy, the robot bops up and down, almost as if he's happy from this compliment. Of course Mood Whiplash occurs with his brethren straight after...
Gamma is one of the few people Tikal interacts with in the flashbacks. While at first terrified of what he might do to the Chao, she calms and apologises when she sees he has no harmful intent, opening up to him about her father. Gamma, a big intimidating futuristic droid (and not even undergoing his Heel–Face Turn yet) is having a bonding exercise with sweet little Tikal from the distant past.
Sonic and Big meet up for the first time during the fight with Chaos 6. Big is fretting over Froggy, who is trapped inside Chaos as his "tail". Sonic instantly makes it his duty to not only get Froggy out of there but give the two time to escape. This has special poignancy since just a moment ago Big assumed to himself that no one would likely bother to save him like he had Froggy.
The opening of Amy's story has her rescuing Birdie from ZERO. Realising Birdie is a fugitive of Eggman, she immediately vows to watch over it.
Amy: Don't worry. I'll protect you. I'll make sure to keep us both out of danger. I'll stand by you all the way.
Near the end of the game, all the other playable characters bring the Chaos Emeralds to Sonic, including the Flicky that was inside Gamma. As an added bonus, he arrives with Amy.