(Warning! This post might contain spoilers and might absolutely suck!)

In my opinion, Chrono Trigger is one of the best games to deliver to the player a sense of choice : each playthrough will be different, from the previous one (Well, if you don't try to do exactly the same thing, that is...).

If you say the good thing that is.
Right after the title screen and the entrance to the fair, you are confronted with a load of opportunities and nearly every action will have a consequence during the trial. It is only then that the player realizes that the story is managed by himself and becomes a semi-author of the story, as the game is still scripted for Chrono (French spelling ;)) is automatically sent to jail.

The biggest thing about this game are the multiple endings: depending on when the player wants to fight Lavos (you can fight him right at the beggining in new game +) and what he has done before, it can radically change the conclusion of this tale.
For example (Major Spoilers !), at one point you are offered to fight Magus to avenge Glenn's friend or spare him, because you know he wasn't totally bad all along although he killed a few people in his process of destroying Lavos. Depending of your decision, either you have a new party member or not. (For me, when this choice was first presented to me, I fortunately created two save slots just in case and so in the first one I spared him, and in the second one I killed him, but immediately after killing him, I felt so bad I turned off the DS...)

One thing I liked a lot is also that some endings are influenced by the sidequests: in the main ending for example, Lucca's mother will either walk or stand on the fountain depending whether you saved her during the sidequest which Chad Concelmo did a Memory Card on http://www.destructoid.com/the-memory-card-55-the-fate-of-lucca-s-mother-122089.phtml

In conclusion, the gamer is the master of the situation in Chrono Trigger and makes in the end his own story.
Ps: If this post absolutely sucked, feel free to send insults, as it is my debuts in the Musing territory