In the best story of the Electrical Superman era(Adventures of Superman 553) Superman is fighting a losing battle against the Millenium Guard. Jimmy Olsen, social outcast at the time, joined by Misa, Ashbury Armstrong, and Scorn finds a weakened Superman against the ropes and decides to carry him to safety in his motorcycle. The episode then turns into an awesome chase through multiple scenarios with Olsen refusing to abandon Superman to his fate, even when the Millenium Guard offer to leave him alone if he relinquishes Superman.
In an issue of Supergirl, Jimmy Olsen saves a kid from an incoming attack by Bizarro Supergirl, while riding on a motorcycle. The kid mistakes Jimmy for a cop or a superhero; Jimmy tells him he's neither, then rushes towards the fight.
In Superman: Earth One, while Supes is cool as usual, Jimmy Olsen gets his own CMOA. When the big bad is tearing apart Metropolis in search of Superman, Jimmy calmly stands in the middle of the destruction, diligently taking the pictures. When the big bad notices and questions Jimmy on this, Jimmy explains that he is willing to risk his life for the truth, and even as the Big Bad is preparing to kill Jimmy, he remains standing, continuing to take his pictures. Luckily for him, Supes takes him down... and Jimmy takes another picture of the wreckage, mentioning the other reason he was out there. To paraphrase, because the truth kicks serious ass.