If you happened to have owned a Sega CD back in The '90s, you're treated—before the game proper even starts— to a beautiful fully-rendered anime cutscene, featuring some spectacular moments just not possible to make on Genesis standalone hardware. Not to mention "You Can Do Anything" playing throughout (or in the North American version, "Sonic Boom").
After the game, Sonic escapes from Little Planet as Eggman's fortress built around it explodes, rescuing Amy and stopping Eggman's plans for controlling time. Right after it's over, Sonic spots Eggman fleeing in his hovercraft, so he grabs a rock, goes into a spin dash, and throws the rock right at him. A few seconds later, the hovercraft (which has already flown into the horizon) explodes, and it's all over... Damn! And this is just the bad ending!
In the good ending, the Little Planet breaks free of the chain and flies off, disappearing in a cloud of sparkles, but not before they form an image of Sonic's head, as if it's thanking him for saving it.
In addition, the scenes after that part that depict Sonic's journey could be described as one huge Crowning Montage of Awesome. Especially the part that takes place in Wacky Workbench, where Sonic lands on one of the badniks, rips its saw blade off while it's still spinning, and forces the other two to ram into each other, all before they crash into a wall.
And let's not forget the intro movie, either. The look that's usually on Shadow's face, wasn't first used in the games by the black blur. It's on Sonic's face in this clip as he glares at the atrocity of the enslaved Little Planet (CMOA for Eggman there too. Chaining down and covering the surface of a PLANET in metal).
Sonic's Super Peel Out technique. Think about it, Sonic's normal speed makes his feet blur together into a circle but at his top speed they're going fast enough that they form what looks like a solid infinity shape/Möbius strip.
The race against Metal Sonic on Stardust Speedway. It was the very first playable race in the series, and thus we had the chance to prove Sonic's speed over Eggman's metallic duplicate. Despite the few number of people who got to play it on the first go-round due to the niche of the Sega CD, it has remained as one of the series' defining moments from the game's release to the present — if not THE defining moment.
The Special Stages were revolutionary for their time: the player was tasked with taking down six UFOs in a confined arena, which one could move about freely in. The scrolling and rotation effects were incredible, if at times choppy. Thankfully, the 2011 re-release touched these segments up so the scrolling and zooming effects were now smooth like silk.
Damsel in Distress, now being able to hammer down Metal Sonic literally.