Hmm, yeah.
First time was when I saw the FMV with Crono being killed. Without the FMV it was a sad scene, but the FMV really improved it. Even seeing Magus' expression, and seeing Schala lieing there on the ground, helped the environment greatly. But what I thought was really awesome, was when Crono remembered Janus saying "One amongst you... Will shortly perish". I couldn't keep my eyes dry watching that.
The second time was some tears of joy during the ending of Chrono Trigger, hearing "To Far Away Times" while watching the Epoch flying through the nightsky. Beautiful. Simply beautiful.
The third time, I believe, was while playing Chrono Cross, that scene with Serge on the S.S. Invincible, after Lynx' attack on Hermit's Hideout, and when he remembers all his times together with Kid. Back then I really loved Serge and Kid together as a couple, and I really thought he cared so deeply about her.
The fourth time, Chrono Cross orphanage scene. Not so much the first part as the last, with Serge and Kid standing on the hill overlooking the flames, with the little Kid saying "Are you going to go away? Are you going to leave me?" and "Your cheek... It's wet...?" With that beautiful music behind it, Star Stealing Girl. I couldn't keep my eyes dry.
Finally, during the Chrono Cross ending. Schala's whole speech and all that, and the feeling of accomplishment, the wedding picture, and the beautiful song Radical Dreamers... Stunning. Simply stunning.
So yeah, I had some emotional moments while playing Trigger and Cross for the first time. I don't know if you can really say crying, but my eyes did go foggy and wet. I don't care if that makes me a sissy or something; I like to think of it as the story being conveyed very well to the player. Kato really did an amazing job. For Chrono Cross too.