With complicated stories and plenty of swearing,the Final Fantasy series is tailored more towards an older audience than the little-kid genre most games are.
Although each game brings its whole new story as opposed to a progression of the last,you can see in each new game what has been borrowed and improved from the last,making each new Final Fantasy game a progression from the previous.
There are in-game characters which tie Final Fantasy games together,eg, in Final Fantasy VIII there is a Namingsway card and a Moggy card,yet these characters are only found in different versions of Final Fantasy.