You can use these to, well, edit your ROM (not that we necessarily condone that). There are several from which to choose.
FF3us Multi Editor
FF3usME can be used with a dump of SNES FF3US for a wide variety of things. It allows you to edit monster stats, monster battle scripts, character stats, colloseum battles, spell stats, monster formations, locations of formations and item stats. You can always find the newest version of this at Lord J's Homepage.
One of the more famous editors, this one can successfully edit world maps and the ingame script. Other editing functions are buggy and may not work.
FF3us Sprite Editor
It edits sprites. Good work figuring that one out, by the way. You can always find the newest version of this at Lord J's Homepage.
FF3SE is another sprite editor that in many ways surpasses FF3us Sprite Editor. It will allow you to modify nearly any sprite in the game. You can always find the newest version of this at Terii Senshi's Homepage.