Getting gold on every license in any game of the series. It's frustrating, mercilessly hard and some tests can make you cry due to constant failure. But as soon as you get gold on the last license test, you feel accomplished. It's truly a great experience.
Driving Missions and Special Events also counts. Very few managed to get all gold on the Sebastian Vettel X Challenge in 5. Fewer managed to do it WITH A DUAL-SHOCK 3.
In Gran Turismo 2, getting all gold on the Super License(The hardest of them all since ALL of the 10 tests focus on time trial.) will reward you the Toyota GT-ONE Race Car. You can already do races that other people couldn't at the start.
This can also apply to GT 3's time trials. Even before you so much as touch simulation mode, you can go beat the time trials, which rewards you with the Panoz Esperante GTR-1, a 588-horsepower racing machine that's fast enough to take on almost anything it can legally enter. Or alternatively, sell it for 500 grand.
The series itself; the popularity of the first iteration proved that sim racers could be widely accessible to a large audience, opening the door for more realistic racing games to co-exist alongside the previously dominant arcade racing genre.
The cinematic intro videos for all of the games. Epic compilations of shots of racing action, showing a wide variety of cars available in the game, combined with equally-awesome songs to make it all the more memorable, and can themselves be a visual summary of passion for automobiles and racing. In the Japanese versions of most of the games, the song is the series' Theme Tune, Moon Over the Castle, which itself has become an iconic staple of the franchise.
The trailers for the games, and other cinematics including the video shown at their completion often also share their awesomeness.
The Spec 2.0 intro in 5, which was shown in games after the huge Spec 2.0 update in 2011, could be seen as an epic comeback of sorts. The original intro for the game is good enough itself. But the new intro features a slightly altered version of Daiky Kaisho's epic 5OUL ON D!SPLAY, which was in the 2010 E3 trailer. The moment of realization that it's that song, could easily make one think that the new intro, featuring some of the new cars and tracks available with the Spec 2.0 update, kicks ass so much that it surpasses the original intro in levels of awesome, especially with the retained build up of live-action footage before the real thing.