Following are the various endings of Chrono Cross which I have located. This list is not yet completed. At this time, one ending that I'm aware of is missing from the list.
Beat the game for the first time without using the Chrono Cross. You only get the normal credits sequence (sans the final crosswalk scene). This was the second ending I received, from what I hear it is many people's first...
Beat the game for the first time by using the Chrono Cross to save Schala. You must use the Chrono Cross sequence to activate the Cross. Includes a monologue by Schala/Kid, the credits (including the final crosswalk scene), and a final FMV of Kid waiting at Opassa beach...
Use the Time Egg at the very beginning of the game, before going to Another World or getting Poshul in your party.
You can obtain this ending by beating Time Devourer as soon as Kid joins your party (I had Poshul in the party as well by this point, using the Heckram Bone at the beginning of the game).
Serge and Leena are back in Arni village; Serge has become a fisherman. Kid goes on to Viper Manor, gets her revenge against Lynx, obtains the Frozen Flame and becomes the new general of Viper Manor. Kid thwarts the Porre invasion and creates the Acacia Empire using the Frozen Flame.
You can obtain this ending by opting NOT to save Kid, and using the time egg as soon as you leave Guldove. At this point, I had Glenn and Leena in the party...
Scene opens in Lisa's shop, where Serge is working. Lisa's father comments that they make a cute couple; Leena comes in, and a bit of a fight ensues between Lisa and Leena. Next scene shows Kid and Norris working in the Viper Manor kitchen washing dishes, Norris refers to Kid as ``Bloody Rose'' and ``Red Scorpion''. Norris has seen one too many spy movies, I think :) Final scene shows Solt, Peppor, and Pierre in Fort Dragonia, mimicking the opening sequence, pursuing Lynx. Solt inquires if Pierre is ``seriously serious about being a hero''. At the end, they play a game of rock-paper-scissors to try to decide who will open the door. ``The three of them were never heard from again...''
You can obtain this ending by using the Time Egg as soon as you return to Home World, after being transformed into Lynx. The party I used consisted of Lynx, Radius, and Harle.
The first scene shows Harle and Lynx in the reconstructed Marbule. They have been there several months, and are on good terms with everyone. A kid even refers to Lynx as ``Lynxy''. The sage tells Lynx he would like to step down as leader, and feels Lynx should lead the demi-humans in Marbule, and try to improve relations with humans.
The next scene shows Radius, Fargo, and Zappa at the entrance to the Sea of Eden, facing Serge. Kid joins with Serge, stating that she'll let nothing get in the way fo Serge's plan. The scene ends with the protagonists facing off against Serge and Kid...
You can obtain this ending by using the Time Egg immediately after rescuing Riddel from Viper Manor, and before Harle leaves the party (so you must do this before going to Hermit's Hideout). The party I used consisted of Lynx, Janice and Irenes.
The first scene shows General Viper facing his troops, who says it is time to face Lynx's army. The ``dishwasher'' Norris can be seen in the back; he comments that he is certain Porre will retaliate in full force. There is a brief scene aboard the S.S. Invincible where shadows are fighting dragoons, and Viper, Fargo, and the Devas face Serge.
The next scene shows Lynx and Harle living peacefully in Marbule, Harle comments that she enjoys ``taking it easy'' and it is the first time she has stayed in one place for so long. Kid shows up thinking Lynx is, well, Lynx... At the end we see Kid facing off with poor Serge, er, ``Lynx''...
You can obtain this ending by using the Time Egg after rescuing Riddel from Viper Manor and after Harle leaves the party. This ending is not available once you acquire the Mastermune, or defeat FATE. The party I used had Lynx, Riddel and Irenes.
The first scene shows Kid and Serge in Chronopolis; Harle approaches and faces Kid, who won't let her pass. Next scene shows a man in Arni attempting to use the Record of Fate... but the Record of Fate turns from green to black on him. This cannot be a good sign. The final scene shows Evil Serge in Chronopolis with the Frozen Flame, and ends with him saying ``I shall become FATE...!'' and laughing maniacally. Not the most optimistic of endings...
You can obtain this ending by using the Time Egg after acquiring the Masamune and freeing Dario. This ending might not available once you defeat FATE. The party I used had Lynx, Riddel and Fargo (interesting that you can pilfer from the Time Devourer...).
Ah, I don't know how exactly to describe this ending except that it is quite amusing. You may have noticed Dario goes to rebuild Viper Manor, well... Viper is now headmaster of a school, turns out he is not very good at making speeches. The rest of the ending shows Serge, Harle and Kid in Another Termina bar -- the Viper Bar, operated by Luccia, Karsh, Marcy, Solt, and Peppor -- oh, and don't forget the muscle, Zoah!
Also included in this ending is the real story behind Starky, via his two comrades who come by Viper Bar. They come in and ask: ``Give us all the liquid substances youu have in this box.'' Later they are heard commenting, ``The creeatures on this planet are rank K... Noo uunique substance can bee deetected in the liquid... Wee must contact the mother ship and beegin our attack at once...'', so THAT's why Starky is here :)
``Huh? Looks like there's an extra 0 on the total there...'' -- Evil Serge, commenting on the bill...
You can obtain this ending by using the Time Egg right after defeating FATE. The party included Serge, Leena and Fargo.
In this ending, the Dragon Gods basically win. The first scene shows the Dragon God meeting with the Dwarf Chieftain and the Sage of Marbule, planning the eradication of humans; the Sage is reluctant... Next scene shows Harle in Arni (now controlled by demi-humans); she picks a flower and visits Serge's grave at Cape Howl... fin.