Released as Final Fantasy 2 originally in North America, this is another game in the franchise that's completely iconic and remembered fondly but actually has a ton of flaws.
While I probably played this game a couple of dozen times as a kid, returning to it as an adult will cause more than a few cringes. Despite the memorable characters and fun gameplay, much of the dialog and plotting is flat-out bad (who can forget such heart felt insults as “You spoony bard?”). But hey, you get to fly a space whale to the moon!
This was also one of the earlier games to feature major character deaths that really stuck with you, as well as villains that you won't soon forget. The music from that battle against the dancing calcobrena dolls thoroughly creeped me out as a kid, and I can still hum it to this day.
If you want to return to the kingdom of Baron and see what happened with Rose and Cecil's kids, there was a direct sequel for the Wii (in the exact same original art style) released in episodic format, with each segment revolving around a different character.