You could try the other Fire Emblem games. I just started Path of Radiance on the Gamecube and it is AWESOME!
If you like Fire Emblem you could always give other tactical RPGs a go. Final Fantasy Tactics was my first and still one of my favourites. It was released on both PS1 (NTSC territories only) and PSP with different translations, but neither translation is especially great. The PS1 version is in moderately broken English and the PSP version is in interminably cheesy faux-Shakespearian. Still, the plot is generally quite good and shines through in spite of the translations.
Speaking of Final Fantasy, that's always a good starting point. Around these parts Final Fantasy IX seems to get the most love. It's a good game and I'd recommend starting with either that, VI or VII. The combat system in most of the Final Fantasy games isn't especially good, though and they have a horrible habit of still having random battles in the build up to dramatic moments that REALLY kills the mood.
For an enjoyable combat system, try the Shin Megami Tensei series. Persona 4 is the most accessible and, to some, best game in the series. For my money Strange Journey on the DS is the best SMT game. Be warned that the different sub-series play very differently in some ways. The "main" games can be compared to Pokemon in that you recruit enemies to fight for you. Except instead of cute animals, they're demons and instead of beating the shit out of them and forcibly enslaving them, you verbally convince them to join you. By contrast, the Persona games have you collecting cards that represent each of the demons and switching them out in battle to use different magic attacks. The whole series is based on an elemental rock-paper-scissors dynamic, with some of them awarding you extra turns for using the right elements at the right time. The storylines are generally quite good, though are somewhat atypical for JRPGs. They're often a fair bit darker, though Persona 4 is an exception, being the happiest game about murder ever made.
Chrono Trigger is one of the best, and most accessible, JRPGs ever. It's got a good plot that doesn't take itself too seriously and is just generally really fun. Fantastic combat system and an awesome soundtrack. Great place to start. Personally I think it's sequel, Chrono Cross, is quite bad but a lot of people really love it.