What I mean when I say Brawl and Madden are the most successful "casual" games is that they are able to appeal to such a large group of people. If you go over to someone's house and they have a 360, chances are they'll have either Madden (if they're really casual) or Halo. They're games that you can play with your friends without any prior experience.
For example, I went over to my cousins house last month. He had gotten an XBox 360, his first system ever. What did he have? Just one game - Madden. Though I've never played Madden on an XBox before then, I picked up a controller and did just fine, and had a blast.
I believe a casual game's goal is to reach a large group of gamers, especially those who either a) don't know much about video games in general or b) don't have the time to play them that often. Actually, the Mario Kart series is a perfect example of a casual game as well. It has enough content to keep the hard core gamer happy, while having that simple thrill that can easily bring in the new gamer.
And usually, they are most known for their multiplayer. For example, Madden, Brawl, Halo, and Mario Kart are famous for their multiplayer modes, not their single player. They are games that are made for multiplayer, and sell because of their multiplayer. And they are made to appeal to every person who has $50 in their pockets.
And yes, Final Fantasy has become more "casual" as the years have gone by. And unlike the stereotype, this doesn't make the game any worse necessarily.