There are quite a few. Most of the times, when one of the popular characters died, it was a sad moment. this holds true even when Yamcha (who was an expert at dying) would die (maybe not always). During the arc of Raditz, at the very beginning of DBZ, the sequential deaths of every character saddened me. Goku’s sacrifice to kill Cell is another incident that was very sad. I cursed Gohan for not killing Cell immediately.
But none of these are the saddest moment for me. I remember being most sad when Goten was first introduced. Towards the end of the episode, clear as crystal, I still remember the narrator announcing “Goten is the son that Goku never got to meet”. That, for some reason, is the saddest I remember being (in the DBZ franchise). I am not quite sure if this will register with others, but I have always really admired Goku’s family, starting with Goku and Chichi’s simple chemistry, to their dedication for their son Gohan (who reciprocated every bit of his parents’ love and care). Realizing that there was another son who Goku had never gotten to know (and vice versa) made me extremely sad.