I mostly like tactical RPG's, as long as it isn't Final Fantasy (no offense ,p)
FFT was alright, but not my favorite.
So some more suggestions, tactics-related:
Vanguard Bandits (PS1) nice story, nice battle system, 3 main story branches so generally you can count on 3 playthroughs.
Brigandine (PS1) my favorite game of all time, hands down. Has some significant flaws (I really want to make something better, that's part of why I got into making games) but it's just
so much fun if you really get into it. Playing Norgard on hard and still defeating the entire Esgares Empire in 12 turns is probably my favorite video-game accomplishment, ever. Important step to proper enjoyment: turn off the 3D visualization of the attacks, they break your concentration on making the right decisions in the battles.
Ogre Battle 64 (N64) I think you may really like this one, it's quite awesome. I wish people still made games like this.
Dragon Force (Sega Saturn) a true classic, though the battles play out very differently than other "tactics" RPGs. May not even fit under the label officially, I dunno, but it has a strategy layer too which lumps it in, in my own mind.
Tactics Ogre (PS1) FFT was basically made from this mold so you may not like it, but it's a significant event in tactics-RPG history and I enjoyed it so I mention it.
Ogre Battle: March of the Black Queen (SNES, I think there's a PS1 version which would probably be better) older than the other two, but still worth a go.
Bahamut Lagoon (SNES) an earlyish take on the genre, has some things I wish had been kept in later tactics-rpg games. Great game, imo.
Arc The Lad Collection (PS1) 1 was solid fun, 2 was pretty impressive, 3 was fun. Come for 2, play 1 first so you have the background story (they tie together), stay for 3 if you like.
And some from other genres:
Star Ocean 2 (PS1) same people as did Valkyrie Profile, but earlier. The battle system is
really fun (so is VPs, and that one is better polished). The story is more lighthearted than VP but I really enjoy them both.
Xenogears (PS1) I'm actually assuming you've already played this, it's on a lot of "of all time" lists, but mentioning it just in case. The execution fell down on the second disk but it's still an incredible experience. With this and a lot of the games on the list you'll enjoy them a lot more if you try to enjoy them, thinking of what was done right rather than what was done wrong.
Lunar: Silver Star Story (PS1) fairly standardish battle mechanics but a very nice story, voice acting, etc.
Lunar 2: Eternal Blue (PS1) even better than the first. One of the most badass scenes/music-tracks of all time lies within, at least if you've played the first one first and sunk into the story.
I'm sure there's more I'm not remembering offhand, but those are good to get started with
so I missed basically anything on the PS1 and before
The PS1 was the golden age of gaming for me. That's largely related to my own personality, etc, but it's how I feel.