I listened to a recent episode of the Retronauts podcast focused on Final Fantasy ROM hacks, hosted by Nadia Oxford and featuring guests Andrew Vestal and my old friend Steve Tramer.
Unfortunately podcasts aren't exactly the ideal medium for helping people find things on the Internet, so I've gone ahead and taken the liberty of putting together a list of the ROM hacks (and at least one fan game) they mentioned, with links.
I haven't played most of these, but FF6 T-Edition is great, and these guys have pretty good taste in 8- and 16-bit Final Fantasy games. Andrew's Unofficial SquareSoft Homepage was the best Square fan site back in the early days of the Web (or at least the best English-language one), and Steve loaned me a fair few Square games back when we were kids. (We, ah, also managed to work FF6's Opera House scene into a Sonic the Hedgehog fanfic we wrote when we were 12, but try not to hold that against us.)
I think these are all the hacks, translations, and fan games they mentioned in the episode, but if I missed any or got any wrong, drop me a line and let me know.