A video showcasing some in game play from the Nintendo DS remake of Final Fantasy III has been uploaded onto youtube. You can see the video:
http://www.youtube.com/watch?v=mzr2C7GotBU
Here. (I tried to embed the video to enable you to watch it here, but the Shin-Ra owners and staff members of this site have HTML disabled. haet.)
The video contains a short cutscene, some exploring, a set battle, a little bit more exploring, a boss fight against a Giant Tortoise creature, and a cutscene with a shiny crystal. The music that plays throughout, especially in the battle, sounds very much like the music from FFIX in it's style. It looks very promising indeed.
[Source: Joystiq]