When both Krypton kids fail their initiation tests, they actually shed tears.
The death of Lightning Lad in Adventure Comics #304 (retold in issue #520). It had been foretold that a Legionnaire was doomed to die stopping Zaryan's invasion. Saturn Girl attempted to sacrifice herself, but Lightning Lad couldn't let her die; so he interfered and got killed in her place. In Saturn Girls' words, he "fulfilled the prophecy, saved her life and broke her heart". All Legionnaires attended his funeral.
Ferro Lad's sacrifice to stop the Sun-Eater. He got blown to smithereens and his death was never undone.
Supergirl rejoined the Legion after "The Great Darkness Saga". She was taking on missions again and rekindling her relationship with Brainiac-5. Nonetheless, a botched mission in Legion of Super-Heroes (Volume 2) #315 made her believe she didn't fit in with the Legion anymore. She said goodbye to Brainiac, leaving the possibility to return someday open, and flew back to the past. Yet still she would never return. Her death hit Brainiac pretty hard.
Monstress's death, and its demonstration of what Jan has become.
In Supergirl and the Legion of Super-Heroes Vol 1 #30, Mon-El appears to give his life in order to put an end to the Dominators. Cosmic Boy gave his eulogy:
Cosmic Boy: ...And he will never be forgotten. We have always said that the Legion isn't a team. It's a movement. In any system, on any world in known space, anyone who is willing to fight for change is welcome to call himself a legionnaire. At last count, we numbered over a quarter of a million. And Mon-El was still the bravest of us all.
In the Justice League/Justice Society crossover "The Lightning Saga" Superman recounts how he and other five Legionnaires volunteered to sacrifice their lives in exchange for bringing Lightning Lad back. His teammates are appalled, in special Bruce.
Batman: You were kids. Superman: No, Batman. We were Legion.
Also: At the end of Legion of Three Worlds, even though they never even knew her, the Retroboot Legion erects a memorial for Monstress at their headquarters. It's a blink-and-you-miss-it thing, but very emotionally satisfying.