There's a really big one at the end of Lucia's quest to find the goddess Althena. What does she find? The goddess', aka Luna's, final message, left when she was a grandmother. The moment you see Luna like that, it just hits full-force: Everyone you came to care for and love in the first game...is gone.
The preceding scene when Nall eulogizes the cast from the first game as well as Luna's sacrifice. Sure we KNEW they were dead, but considering how likable the cast of the first game was, it makes it more painful to accept.
There's also Lucia's reaction to all of it in general. The look on her face when she first sees an aged Luna shows just how painful the very concept of Althena being gone is, and how completely betrayed she feels.
This is also the scene that causes all sorts of speculation about just what their relationship was. Lucia's expression and reaction is less that of finding out a "coworker" is gone and more one of finding out a loved one has been stabbed through the heart.
The entire scene where Ronfar saves Mauri.
The scene where Ruby has to accept the power of the Red Dragon and come to terms with the fact that she'll outlive her friends. It's worse if you're a cat lover.
Ruby: I don't want to grow up, Hiro! I don't want eternal life! I want to be with you forever! I don't want to be alone! Hiro: Ruby... Don't you understand? it's up to you to decide whether you'll be alone or not! Ruby: What do you mean? Hiro: Didn't you hear Nall? Every day we spend together, we're making more memories. And those memories will always brighten your heart and take away your fear. You've lived with me since I was a little boy, Ruby. And you've spent plenty of time with our new friends. Your heart must be bursting with memories by now, Ruby! And as long as you have those memories, we will always be with you. You'll never be alone. Ruby: I always pretended not to hear the voice inside of me. The voice that kept asking when I was going to grow up. I knew that I would have to become an adult to protect our world... but I didn't want to lose my friends. So I ignored that voice, no matter how loud it spoke. But now I know that I won't lose you. I won't be alone. I'll always be with all of you, whether it's in the real world or in my heart. I won't ignore that voice anymore. I'll let it tell me what I need to do...
Hiro's reaction alone to all of this, and especially his anguished cry as she's fading away, are enough to make you reach for the tissues by themselves. Combine them with Lucia's side of it, and you should be blubbering even before she leaves.
The final scene of the Playable Epilogue. Lucia's tears of joy upon seeing Hiro on top of that crystal-thing of hers will likely inspire similar tears in the player.
In the pentultimate cutscene of the Playable Epilogue in the PS1 version, the other party members say their farewells to Hiro; as heartwarming as Hiro's reunion with Lucia may be, seeing what he is giving up to see her again adds a bittersweet edge to this. While Leo is philosophical and Ronfar remains fairly upbeat, the very real possibility that they may never see Hiro again has a deeper effect on the other three; Jean puts on a brave face as best she can, Lemina tries to do the same but with less success, and Ruby, who has by far the strongest emotional attachment to Hiro, breaks down completely.
Ghaleon's death. "Are you watching in secret, Dyne? These children shine with your light..." *sniff*