The new Chrono Trigger for Nintendo Ds offers a range of unlockable alternative endings, so here's how to get them:
Final ending #1 "Beyond Time": Defeat Lavos after re-launch Crono at Death Peak.
Final ending #10 "Dino age": Defeat Lavos after facing Magus, but before facing Azala.
Final ending #11 "What The Prophet Seeks": Defeat Lavos after facing Azala, but before Schala opens the sealed door.
Final ending #12 "Memory lane": Defeat Lavos after Schala opens the sealed door, but before you restore the light for the pendant.
Final ending #13 "Dream's Epilogue": Defeat Dream Devourer beyond Eclipse's Time
Final ending #2 "Reunion": Defeat Lavos while Kronos is dead.
Final ending #3 "The Dream Project": Defeat Lavos in Ocean Palace or immediately after the start of a new game.
Final ending #4 "The Successor of Guardia": Defeat Lavos after saving Leene and Marle, but before going to the end of time.
Final ending #5 "Good Night": Defeat Lavos after visiting the end of time, but before returning to the Middle Ages.
Final ending #6 "The Legendary Hero": Defeat Lavos after his arrival in the Middle Ages, but before getting the Heroes badge.
Final ending #7 "The Unknown Past": Defeat Lavos after receiving the Hero of the badge, but before the key to the gate was stolen.
Final ending #8 "People of the times": Defeat Lavos after regaining the gate key, but before giving the Masamune to the frog
Final ending #9 "The Oath": Defeat Lavos after giving the Masamune to the frog, but before the fight against the Sorceress