You can't go wrong with Tales.  Lost Odyssey is also really good.  Tales has a more frantic battle system, while Lost is slower and turn based.

Tales, all the way

I voted for Tales of Vesperia, then noticed that Eternal Sonata has no votes. This is a travesty. That game is amazing. Someone vote for it, damnit.

I never finished Eternal Sonata. It got draggy and boring, but the combat system was interesting enough. Lost Odyssey was fantastic, though a bit old-school. I didn't like The Last Remnant at all, really. I can't remember why, but I didn't get more than a few hours into it. I'm still in the middle of FF13, and I'm enjoying it to a point. It's very linear. VERY linear. I keep hearing that it opens up later, but so far it hasn't.
 
Generally when someone asks about a JRPG to play, I just tell them Lost Odyssey.

The only 2 I've played are Blue Dragon and Eternal Sonata. Blue Dragon felt kind of dated, but Eternal Sonata was a really interesting game.

I really enjoyed Tales of Vesperia, this is saying a lot seeing i absolutely cannot stand Anime, and it was only the second JRPG i ever played.

Since you can find most of these games for $15 or less, it's hard to make a real dud of a purchasing decision. My vote went for Lost Odyssey, but I didn't play Tales. Eternal Sonata is worth checking out too; it seemed pretty unique to me, a fairweather JRPG guy.

I'd say blue dragon or eternal sonata because they are both very good games.
I'd also say that although I didn't find lost oddysee to be that good, I'd advise trying it because everyone else seems to like it, and I could see that it was very good, just to me something didn't feel quite right.

I voted for Lost Odyssey. Sad to see Mistwalkers next game "The Last Story" is Wii only. For some reason I don't seem to be able to get into long games on the Wii. I guess with Dragon Quest X and this I'll have to dust it off though.
Eternal Sonata is also really good. Sad to see it hasn't got many votes. As others have mentioned its well worth checking out.

My vote is for Lost Odyssey. I enjoyed that game more than any JRPG I have played in a long, long time. Fantastic characters, story, and a non-teenage non-plucky protagonist. 
 
Having said that, I own but have not currently played (for longer than a couple of hours) Resonance of Fate, and that game seems like it could be something special also. The gameplay is really unique and for my money it makes the best attempt  to change up the battle formula of a JRPG that I have seen. I cannot really speak for the story of that game, although by all accounts it is at the very least an enjoyable tale.

Either Lost Odyssey or Tales of Vesperia. You can't go wrong with either one in my book.

there aren't good jrpgs

  What?  No love for Enchanted Arms?  But how can you possibly say "no" to a game with this character in it?

" Resonance of Fate is not only the best JRPG on the 360 but the best game I've played for ages.  "

^This

" Either Lost Odyssey or Tales of Vesperia. You can't go wrong with either one in my book. "

If playing FF13 on the PS3 isn't an option, then I'd say it wins pretty easily; it's the most interesting HD JRPG. Lost Odyssey is a decent game, but very hidebound.

Lost Odyssey was the most boring game I've ever played in my life. Battles were so SLOW, character designs were awful and the whole game was clunky in general. Only good bit was the story/poem snippets and the voice acting. Those however are not enough to save a dull game - publish those short stories in a book and I'd gladly take that instead. Why should I have to chug through tedium to experiance those excellent short stories? A book would have made a lot more sense.
 
My choices:
1) Tales of Vesparia
2) Resonance of Fate
3) Final Fantasy XIII

Tales of Vesperia and Resonance of Fate are the best, although the latter might give you some frustration due to the difficulty. 
I've heard good things about Lost Odyssey and I've wanted to try it out myself, so I'd say look into it.
FFXIII has had mixed reviews. I didn't buy it myself but my sister did. She recognised problems about the characters not being great and the story being confusing, but she liked it overall.
Avoid Star Ocean 4. There are almost no likeable characters, the plot was boring and the gameplay just didn't work for me. 
Eternal Sonata has a good soundtrack, but the gameplay gets a bit repetetive and its short. Its just a filler RPG really. 
 
The rest I don't know about.

If what you like is turned based with great graphics you cannot go wrong with Lost Odyssey. 
Just make sure you install the game to your hard drive or you are gonna bitch about the loading. If space is an issue, just install one disc at a time.

Final Fantasy XIII, as much as I tried to like Tales of Vesperia it felt a bit too outdated for me. Despite all the flaws with Final Fantasy XIII gameplay and story wise, every single frame of that game screams production value and that was enough to get me to stomach through it.

" @Shadow: Should I be ashamed to say I got pretty far into that game and only didn't complete it because my 360 red ringed and I just got a new one (hence losing the save?)   Also, Lost Odssey is the ONLY correct answer. "

I played all of them.. cept'  Infinite Undiscovery and Spectral Force 3 ... and oddly i liked Enchanted Arms the best :)  (it was a long time ago.. around xbox launch)
 
but.. at the end of the day.. i might not be the best person so suggest a jrpg.. as i always hit a point in them when i'm like "wtf are wrong with the japanese.. these games suck! fucking random shit... emo chars... retarted, pointless and drawn out stories... ugh!" 
 
lost oddessy and blue dragon were ok too. 
 
ffXIII was ass... ugh.. "oh... after 15-20 hours it gets good.." well.. i think i made it to around 15 hours (on the p3) and i just couldn't take it anymore :)

What about Nier?

Lost Odyssey or Final Fantasy XIII for me.

I voted for Eternal Sonata. The art style totally blew me away. It's childish style but really special...i can't describe. Also although i played most of the other games on the list i think Eternal Sonata had the best fighting system. My second choice would be Lost Odyssey. The fights were really challanging which i found very motivating. But somehow the story and art style didn't impress me that much. I also want to say that Tales of Vesperia seems to be cool. played it for some hours, LOVED the art style but hated the fighting system...just not very satisfying to me

Lost Odyssey blew me away when I played it. I believe that it is a hugely underrated game and if you like JRPG's you should give it a try. Its cheap now as well.

Eternal Sonata is a solid game but I probably couldn't recommend it. I almost had to stop playing when two of the main characters (2 brothers who steal bread and give it to orphans or something) had basically the following exchange.

Shitty little brother character: "Hey bro, why do we have to steal bread? Why can't everyone just have bread?"

Cool older brother: "Because taxes"

SLBC: "Why would they put high taxes on things that people need to live?"

COB: "Taxes are bad"

SLBC: "We should do something about this"

COB: "Let's go to the King and complain about taxes"

Game's OK to play but the story is pure assgarbage.

@Atlas said:

I voted for Tales of Vesperia, then noticed that Eternal Sonata has no votes. This is a travesty. That game is amazing. Someone vote for it, damnit.

You're welcome!

I've actually only tried it for like three hours, but it seems fantastic.

@PK_Koopa: About Eternal Sonata, how short is "short" in this case? 'Cause I really enjoyed what I played of it and my main issue with most JRPG's is that I have trouble finishing them because of their lenght (sometimes pacing). I would actually be more inclined to go out and get it if I could finish it in say, 30 hours?

Voted for Vesperia. The sad life of a European yearning for Tales of- games, the first one I really got to sink my teeth in. Lost Odyssey is fantastic but the main plot got too silly for me. Stuff like Kakanas in his underwear felt really out of place after reading a beautiful short story too.

Really wanted to like The Last Remnant but it was made impossible especially towards the end, you need perfect squad composition to make it through. Can't fault a game for being challenging but I got slapped so hard I thought the enemies were 15 hours further into the game than me.

I haven't played any 360 JRPGS however as a PS3 owner out of the list of 360 games I'd play Lost odyssey and Tales come to mind. Lost Odyssey would come first.

Tales of Vesperia is amazing. The characters are far more likeable than lost Odyssey 

wut about ff13 

I gave my vote to Tales because it more closely fits my expectations for a traditional JRPG (as someone who only started playing them this generation--I know, I'm backfilling the PS2 era slowly), but definitely give Resonance of Fate a look as well. Very stylish, far fewer ridiculous anime tropes, more likeable main characters (ugh Karol) and a battle system that's just as good, if very different (though Vesperia's battle system has a lot more depth to it). The place where Resonance of Fate really falls down is the plot, which is told to you in fragments and barely makes any sense the first time around. It's also more episodic, and thus lacks the epic adventure feel of Vesperia--this is either a plus or a minus, depending on your tastes.

I've only played Lost Odyssey and Eternal Sonata.

Both are really great games, but I like Eternal Sonata just a bit more.

Resonance of Fate.

@ashkanhoss29: Same here.

I'm a big fan of Blue Dragon (I'm currently 53 hours into it). I'm planning on picking up Tales of Vesperia soon. However, the cheapest place to get it in the UK is on the XBL Marketplace - which is a shame :( 
 
I might try Lost Odyssey

I'm a big fan of Blue Dragon (I'm currently 53 hours into it). I'm planning on picking up Tales of Vesperia soon. However, the cheapest place to get it in the UK is on the XBL Marketplace - which is a shame :( 
 
I might try Lost Odyssey

My favorite is playing the role of Agent Francis York Morgan.

I only played Lost Odyssey (which was the first JRPG I ever played) and I thought it was pretty good. I have heard good things about Tales of Vesperia, Eternal Sonata, and Resonance of Fate, but I havent had a chance to play those games yet.

Lost Odyssey has my vote.  It's an awesome game.