Squaresoft had a golden era in the 1990s. As someone who is just starting to realize that he's not exactly "young people" anymore, I sometimes forget that there are people who are legitimately adults who don't really remember the 90s.
The SNES era saw the release of Final Fantasy VI (released as III in the US as there had only been two of the five games released here at that point. For VII they just synched up the series with Japan,) Secret of Mana, Super Mario RPG, and Chrono Trigger. Of these, I really played a lot more Mario RPG and Secret of Mana when I was a kid, but in college, I got the PS1 port of Chrono Trigger (played on my PS2, so it was kind of doubly removed from its original form) and I realized it's one of the greatest games of all time.
And one of the reasons that it was so good is that they managed to create a solid time-travel narrative that was not impossible to follow.
Time Travel is, hypothetically, one of the coolest subjects in fiction, but writing it is very, very hard. For one thing, because it's a totally hypothetical thing that may be not just physically impossible, but actually metaphysically impossible if fully considered, the logic surrounding it has to be worked out by the writer. And it's easy to slip up and be inconsistent.
Now, to be fair, Chrono Trigger is not always perfectly consistent - generally, the party members are immune to changes in the fabric of history, allowing them to remember other versions of events before they changed them. However, there's also a part where party member Marle disappears from existence because her ancestor was kidnapped and presumably would be killed without further intervention.
Still, as interesting as it is to talk about the logical paradoxes that can arise from being able to manipulate the events of history, one of the other really great opportunities in a time-travel narrative is to see how familiar things change.
For example, the game starts in the modern era in 1000 AD (the years are a little misleading, as 1000 seems more like 1990, and 1999 looks like some kind of futuristic civilization even though the game was made only a couple years before that in the real world.) In 1000, there is a town full of beings that look monstrous, but they're perfectly friendly. However, when traveling back to 600 AD, there is a war between the human kingdom of Guardia and the Mystics - those very same monsters that will be friendly in the present. In fact, when the game begins, the leader of the Mystics, known as Magus, looks like he's going to be the main bad guy of the story.
One also gets to play some fun games with long periods of time. One of the party members is a robot from the future, and there is a side-quest toward the end of the game in which you can have Robo (ok, the character names are not the most creative) start working on irrigating and planting trees in a desert and then quickly traveling several hundred years into the future and picking him up when the job is done.
I don't think I've seen any other games pull off time travel as well as Chrono Trigger. Time Splitters: Future Perfect did have some fun with it, but not nearly to the same degree.
Chrono Trigger had one sequel, Chrono Cross, which I never played, but it never grew into a large franchise like Final Fantasy (or Secret of Mana, which I actually think went on to have several games, even though I'm almost utterly unfamiliar with anything but that one.)