Well all of the Final Fantasy games aren't connected story-wise. They happen in all of their own universes and everything. Final Fantasy XIII is about 6 people who fight back against the people who enslave them and force them to destroy the world. It's pretty neat.
Now, I'm playing Final Fantasy IV. I haven't finished it yet, but it's about a kingdom who is controlled by a mysterious man and the protagonist from the same kingdom teams up with people he meets from other kingdoms along the way to right defeat the new leader of his kingdom and right the wrongs that he's done while still loyal to his home-kingdom.