Chrono Cross has 11 endings in all, most of which are available only after beating the game the first time and starting a new game under the "New Game +" option. Here is a list of the endings. You can also download a text file of them here.
Chrono Cross Endings
1) Schala's Death: Beat the Time Devourer without using the Chrono Cross. Lavos and Schala die together and are disintegrated. The credits start to roll and some of the game's cinemas can be seen next to them. Among those cinemas are a few new ones, where you can see live-action footage of a girl dressed in white, searching for someone. Who is this girl?
2) The Song of Life: Beat the Time Devourer by using the Chrono Cross properly. Lavos dies but Schala is separated from him at the last minute and survives. Schala is happy to meet Serge and she decides he has suffered enough and sends him home. He will forget everything that has happened. Kid wants to stay with Serge and she promises to look for him no matter what time period he is in. Serge wakes up on Opassa Beach. Leena is there but doesn't understand what Serge tries to tell her. Something about some place called Terra Tower. Without FATE controlling their lives anymore, they will now lead a happier, normal life. A cinema is shown where you see the same book from the intro cinema. Kid is the one reading the book, and as the book closes, the camera zooms in on a picture of Schala "Kid" Zeal next to a male figure. The credits begin to roll and some of the game's cinemas can be seen next to them. Now you see more of the live-action girl dressed in white. She is Princess Schala "Kid" Zeal and she's searching everywhere for Janus, better known as "Serge." After the credits, you see one last cinema of Kid dressed like a princess as she stares into the ocean. This is the "true" ending of Chrono Cross.
3) Meet the Development Team: Beat the Time Devourer with only Serge in your party at the beginning of a New Game+. You appear in Viper Manor, where you can talk to the development team responsible for making Chrono Cross. Some of them also worked on Chrono Trigger, like Yasunori Mitsuda who composed both of their soundtracks. Speaking of soundtracks, this ending gives you access to a sound test, 67 tracks in all! You can also talk to Kid and change all of the characters names. Where is she? She's hiding in the same room where you get the sound test.
4) Serge: The Great Fisherman - Kid and the Frozen Flame: Beat the Time Devourer before infiltrating Viper Manor. Serge returns home from a fishing trip and meets with Leena at the pier, where they talk about Serge's awesome fishing techniques and the possibility of them getting married. Then you see Kid entering Viper Manor by herself, where she kills Lynx and steals the Frozen Flame. As the new Lord of El Nido, General Kid and the Acacia Dragoons conquer neighboring countries with ease. Next stop, Guardia Kingdom.
5) Serge gets a job - Pierre: a real hero?: Beat the Time Devourer before Serge turns into Lynx. Serge gets a job at Termina's Element shop. Lisa, Funguy's daughter, is very happy to have Serge around. Leena enters the shop and the two girls start insulting each other, fighting over Serge. Leena leaves, outraged. Then Kid enters and is insulted immediately by Lisa, who calls her ugly. Surprisingly, Kid is bummed out big time by this. The scene shifts to Fort Dragonia where Pierre, Solt, and Peppor are attempting to defeat Lynx. Just when they are about to face Lynx, Pierre starts faking a stomachache. The three of them where never heard from again...
6) A Magical Concert: Beat the Time Devourer before Serge turns into Lynx. (Nikki and Razzly must be in your party) The Magical Dreamers are going to perform in Termina, as part of the Viper Festival. Leena and Lisa are running late because Lisa forgot where she put the tickets. Nikki introduces the new members of the band: Serge on percussion, Kid on vocals, and Razzly as the mascot. While everyone is having fun at the concert, Lynx is at Fort Dragonia doing as he pleases since no one is there to stop him.
7) A new Marbule - Dragoon's Vengeance: Beat the Time Devourer as Lynx, before rescuing Riddel from the Porre Army. Serge, with Lynx's body, helps the demi-humans in Marbule lead a happier, more prosperous life. Harle is there to help too. The Sage asks Lynx to be the new Sage of Marbule. The scene shifts to Death's Door, where Radius, Zappa, and Fargo are about to face Dark Serge in battle. Serge killed all of the Acacia Dragoons and now it's payback time. But Serge has a secret weapon: Kid.
8) Dragoon's Pride - Kid's Quest: Beat the Time Devourer as Lynx, after rescuing Riddel from the Porre Army, but before Harle leaves your party. General Viper and the Acacia Dragoons get ready to face Dark Serge. Norris has been spying on them, dressed as a cook, and will make a report to the Porre Army. The Dragoons find Serge on board the S.S. Invincible, which is crawling with monsters. Fargo teams up with the Dragoons, but Serge couldn't care less. The scene shifts to Marbule, where Serge, in Lynx's body, is enjoying a nice conversation with Harle. She's going to cook a nice meal for Lynx but Kid interrupts her and challenges Lynx to a duel. The dialog here varies depending on what you answer when Harle asks what you want for dinner.
9) The Darkness Prevails: Beat the Time Devourer as Lynx, before defeating FATE at Chronopolis. (Without the Mastermune) Dark Serge and Kid enter Chronopolis. Kid senses danger and tells Serge to go on ahead. It was Harle who was following them. Harle doesn't want to fight Kid, but she has no choice. The scene shifts to Arni Village, where an old man wants to use Arni's Record of Fate. When he's about to use it, it turns black and the man panics. This happened because Dark Serge found the Frozen Flame in Chronopolis, and now he will become FATE.
10) Viper Kindergarten - Alien Revelation: Beat the Time Devourer as Lynx, before defeating FATE at Chronopolis. (With the Mastermune) Viper Manor is full of kids. Dario suggests to "Headmaster" Viper that they should start a Dragoon youth group. After all, these kids will be the future Dragoons of the great Acacia Empire. Just don't let Lady Riddel find out about this. The scene shifts to Termina, where Dark Serge, Harle, and Kid decide to rest at the bar. Luccia, Marcy, Karsh, Solt, and Peppor are all employees there. Harle orders a "Denadoro Mountain Blend" with cream and extra sugar. Kid orders the bar's special drink, the "Galaxy Night." Serge wants a beer, but because he's inside a 17-year-old body he can't have any alcohol, so he orders a "Galaxy Night" for him and one for Marcy. Then two little aliens from Starky's race enter the bar and ask for all liquid substances available. They say humans are rank "K" and they will now get ready for a full alien invasion on El Nido. Starky's mission was to study humans, then kill 'em all! It turns out Serge doesn't have enough cash on him to pay the check and he's taken to the back room of the bar, where Zoah is gonna beat some sense into him.
11) Wrath of the Dragon Gods: Beat the Time Devourer as soon as you defeat FATE at Chronopolis. The Dwarf Chieftan and the Sage of Marbule get together at Sky Dragon Isle, where they are planning the annihilation of all humans, along with the Dark Moon Dragon. The Dwarf can't wait for the bloodbath to commence, but the Sage of Marbule is not so sure that this is the right thing to do. The Dark Moon Dragon, also known as Time Devourer, will stain the planet with the blood of humanity. The scene shifts to Arni Village, where the demi-humans now live. Harle is there and she feels terrible because of what has happened. She misses Serge, and she brings flowers to his grave at Cape Howl.