Woah, I forgot to list Chrono Trigger! Really an honorary Final Fantasy game.
I really liked Shadow of Destiny too. It's a really unique premise. For one thing, it's a murder mystery, which is unusual in itself for a game...but the murder you're trying to solve is your own! You keep being brought back to times earlier and earlier, and keep failing. It involves time travel, and a really creepy plot.
Here's the link to Nethack by the way (it's free):
http://www.nethack.org/
It's always on the top 10 lists of the best games ever from good game sites. It basically just uses ascii characters as graphics, so I know it's hard to get into it. But once you do, there is SO MUCH DEPTH to it. There's so much you can do.
It's the precursor to games like Diablo or Champions of Norath, except it's way better than those games. There's so much more in it. More to find, explore, more abilities to use, more freedom to tackle the game the way you want to, etc.