One of the earliest Awesome Moments in the series: In the Green Hill Zone, you come across a pipe-like cave that Sonic automatically spindashes into. You emerge into a checkpoint, spindash into another pipe, and are launched 100 feet into the air into a huge pile of rings! Those kinds of game physics demonstrations in the 16-bit era were hard to come by.
Jumping and spinning at the right time on the loop before the tunnel can make for an awesome, disturbing and annoying moment all at once. It sends Sonic going even faster so that if you don't jump at the right time, he'll die when he hits the bottom of the screen much like he would a Bottomless Pit. Essentially going so fast it kills him.
Even ignoring all the quarter-pipes and loops, just the terrain of Green Hill Zone was far more natural and varied than the norm of the era, with different kinds of subtle and not-so-subtle slopes all over the zone.
After Scrap Brain Zone Act 2, there's a brief transition where Eggman hits a switch and sends Sonic falling down into a pit that leads into Act 3. How many video games had transitions back in 1991!?!
Final Zone as a whole is this; Sonic has to deal with Robotnik trying to crush him alive in an enclosed space with minimal rings! And he wins!
In the remake, through the level select, you can do a few things that can't be done normally - Like making the seventh Chaos Emerald to show up, allowing you to go Super. Even with Tails, who previously needed the Super Emeralds.