Through all of its ups and downs, the games in the Sonic the Hedgehog series have been (and still are) so chock-full of awesome moments, each game has its own page (feel free to start pages for other games):
Essentially, every time Sonic goes super in the series is such a moment. The transformation sequences from Sonic Heroes and Sonic the Hedgehog 2006 are among the best ones. Regardless of the rest of the games, Sonic unleashing a huge Battle Aura around himself and turning the iconic golden color as the game's theme song plays is pretty damn incredible.
In the games where you have to collect the emeralds yourself via special stages, the moment when you get the last one definitely counts. And if it's one of the games where you can go Super Sonic in normal gameplay (so basically every Sonic game after Sonic 3 & Knuckles and before Sonic Colors), seeing the "NOW SONIC CAN BE SUPER SONIC" message can make you feel particularly triumphant.
Sonic's surprise appearance in the Subspace Emissary is a crowning moment in itself, as he manages to charge up what appears to be the Ancient Light Attack to smash Tabuu so hard, his wings shatter and his Off Waves are interrupted.
Heck, his introductory video, posted on the site when he was first revealed to have made it into the game, was a minute-long moment of awesome for him. Imagine the fan's thought process as he watches this video: Mario's there, he's beating up some Goombas, who's that running? Oh my god, it's those shoes. Oh my god, it's HIM. The 'hog himself blasts Mario out of the way, boasts "Sonic's the name, speed's my game!" "Live and Learn" kicks in. The rest of the video consists of him beating the crap out of several other Smashers (and pulling a victory pose with Mario, finally putting an end to their lifelong rivalry) before going Super Sonic. Indeed, many a fan had a fangasm as they watched this video knowing that their wet fanboy dreams would finally come to fruition.
Even Snake's introduction video showed him in a two-sided battle, but Sonic never got a scratch in his.
Even if Sonic has hit some low points in his series, he's still been with us for 20 years. Somehow he and other characters in the series have endeared themselves to the general public and kept going after all this time. He has been a character that has appeared a wanderer and goof-off, but will still work as hard as he can to reach his goals (mostly saving the world), often with the help of some pretty cool friends, and great music in the background. So maybe some of the games aren't that great, but seeing any moments listed here (or ones that haven't been listed yet) will always make that kid in us happy to see a hero just one more time.
The Progressive and Nike commercials. Sonic is finally regaining his place at the top of the gaming industry. It's nice to see Sonic becoming popular outside of the gaming industry, just like the old days.