Merely existing. Look at it this way: Kuuga was able to bring back the Kamen Rider brand out of limbo and help launch it into the mega franchise it is today. Only a truly awesome show could do that.
Another meta example: The Kuuga Curse (in which any attempt at translating the series gets cancelled sometime after the tenth episode) being broken by Midnight Crew Subs after 10 years of being subbed. This even prompted TV-Nihon to resume their long-abandoned translation.
Many of Kuuga's fights, but a few take the cake.
Kuuga's bike-on-bike battle with Go-Badaa-Ba.
Any time he masters a new form for the first time is a memorable moment.
Transforming to Mighty after a rousing speech about what he's decided to fight for as a church burns down around him, Ichijo, and the Grongi they're fighting.
Showing off some impressive moves combined with acrobatic skill when he finally learns he needs the rod for Dragon form.
Mastering Pegasus by snatching the bee-like sniper monster's projectile out of midair then one-shotting it with his own blaster. The Grongi screams like a little girl in fear.
Titan's debut features Kuuga no-selling the monster's explosive spitting attack while slowly advancing on it, stopping the last one with his hand and then running it through with his sword.
Episode 35. Kuuga delivers an unbelievable smackdown to a monster that really, really deserves it.
To wit: After finding the Grongi in the hospital, Yusuke transforms while running at it, tackles it out the window, and then just starts pummeling its face in, screaming the whole time. Once it starts to fight back he summons Gouram and then rams it, driving the Grongi all the way to the lake on the front of his bike. The monster tries to kill Kuuga by stabbing him close-range but Kuuga sees it coming and transforms to Titan, shrugging the attack off. When he gets to the lake he comes to a screeching stop, throwing the Grongi into the water. Then he draws his sword and slowly walks toward the monster (who is whimpering in terror at this point), silently transforming to Rising Titan, then slashing the Grongi and finally knocking it on the ground and impaling it there, after screaming during that curbstomp as well.
It also dips into Nightmare Fuel, as the scene is meant to draw concern for Yuusuke's psyche. Up until this point, we never really saw Yuusuke actually get angry. He's always nice and likes to make people smile. Then his button got pressed.
Ichijo deserves a mention for his sheer dedication to his job even when badly injured. He also is the only normal human in the series to take out any Grongi.
Episode 16: Kuuga does a finishing move on a truck so hard that it somehow kills the Grongi driving it!