I'm a big fan of the side quests in Chrono Trigger. Going back and forth through time in order to change things was very interesting! I liked leaving Robo in the past only to come back to the present and find the world map had a full forest where a desert used to be. I also liked seeing Cyrus' ghost, which was a great part of the game for Frog's storyline.
What video games do you think had great side quests, and what did you have to do?