Nobuo (and therefore FF music) is great. Some examples:
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His early work on the first Final Fantasy games lasted long because, in a similar spirit to Mario music, it was fun. The Chocobo theme is a perfect example (though some recent FF games have tried stylizing the theme to various genres, which is cool, but often sounds strange). Fanfare is famous, too. I don't have any links, though, because they're all just short loops.
Starting with FFVI (which is when the FF series first tried a dark storyline, he started changing his musical style. The music lost some of its fun, but songs became longer, some were full masterpieces, and he still tried to keep his tunes memorable:
Though I think FFVII is far overrated as a game (spectacular story, but so-so gameplay), its music is
the best, featuring one of my favorite video game themes of all time:
The FFVII World Map theme.
And though we should be thanking whoever coordinated the video so well to the music,
the opening video for FFXII is perfect. What you hear for the first 40 or so seconds is the original Final Fantasy theme, actually.
I believe he also wrote most of the
Super Smash Bros. Brawl theme.
Also known as ExpHP everywhere else.