I've played most of the games in the series and will comment on them in order of release:
Phantasia: Played about a third of this one. It was a technical marvel around the time it was released for the SNES but hasn't dated terribly well. Still fun, though.
Destiny: Phantasia's big PSX brother. The only thing I really remember about this game is that the story was really trite. Battle system is very similar to Phantasia's so if you liked it, you'll probably like Destiny's.
Eternia/Destiny 2 in America: Like Destiny, only longer and prettier. Again, story and characters not much to speak of but the music is probably the best of the series and the battles remain a blast. Of the three 2D battle-system games, this one is the best.
Destiny 2: Haven't played, Japan-only.
Symphonia: For the RPG-starved Gamecube, this game was a breath of fresh air. Characters are JRPG archetypes but entertaining enough and the rest of the game has held up well (probably even better with the remake coming out). Recommended.
Symphonia: Dawn of the New World: I made it about a third into this before barfing. It's absolute trash, with two of the most annoying "heroes" in a JRPG. The story isn't much better. Worse, everything else is a lazy regurgitation of the first game, as you'd expect, from towns to music. Avoid like the plague.
Rebirth: Haven't played, Japan-only. I hear it's terrible, with the worst story in the series (and that's saying something).
Legendia: Didn't play much of this one. Found the battle system sluggish and the story really, really dull. Music's great though, the only game not composed by Sakuraba.
Abyss: Probably my favorite Tales game, if you can get on board with the (deliberate) obnoxiousness of the main character, there's a lot to love here. There's actual, reasonable character development in this game and for a JRPG, the plot is surprisingly in-depth and credible. There's a lot of backtracking later on but I was held in the story's grasp by that point and didn't mind. Battles are great, music is decent. Definitely a must-play.
Innocence: Japan and DS only. I played a bit of this. It's pretty awful.
Vesperia: Probably the best JRPG released on the 360, this is a really solid game. The main lead is refreshingly original, the rest of the characters a lot of fun and while the plot isn't terribly original, it gets the job gone. The game also looks gorgeous and has a terrific and challenging battle system. Recommended.
Hearts: DS, Japan only. Haven't played. Heard it's okay.
Graces f: I managed to beat this game, god knows how. It has one of the worst plots in a JRPG with stupifyingly dumb characters. You'll want to smack the lead every time he opens his mouth and most everyone else isn't much better. It's not a good sign when the characters are more tolerable in the children segments (you start the game in earlier times) than they are as adults. A lot of people claim the detailed battle system makes up for a lot of sins and it does at first but the game goes on forever and what was once original becomes stale the longer you try to tolerate the things the characters are saying.
Xillia: Haven't played yet. Was too burnt out on Graces.
The music in the series gets progressively worse with each game, Sakuraba on auto-pilot (as he's been for years now). He reportedly doesn't get much time to write the music and it really shows. I've heard Xillia is more inspired but haven't heard for myself yet.