Although Chrono Trigger doesn't sport a huge cast of characters like the sequel, you still grow to love them real quick. I can guarantee that you will never forget these characters, Square did an amazing job with character development in this game.
Crono: The protagonist, you never see him talk (except for one of the endings), he has a great balance of attacks and techs. You'll want to stick every tab on him.
Marle: A real looker, Crono bumps into her very early in the game. Although she is kinda valley girl-ish, she comes in handy.
Lucca: Crono's childhood friend, she is a brillant scientist/inventor. Her telepod gets you tangled up in this whole mess.
Frog: Don't let his frog-body exterior fool you, he is a master swordsmen. His past is full of hatred for Magus.
Robo: A humaniod robot from the future, he is very strong, his magic tech's suck, but his physical tech's are very powerful.
Ayla: Chief of the Ioka Tribe circa 65 Million B.C., although not bright, she has a strong sense of justice.
Magus: An Evil sorcerer from the past, he leads a war of undead against the Kingdom of Guardia.
