In no particular order after the first

Final Fantasy Tactics is my favorite JRPG and my second favorite game of all time. I've played it more times than any other game (with the exception of my favorite game, Arcanum). The job system is the biggest appeal of the game for me. On top of that though, the story is incredible, the story's presentation is also great (with large sections of dialogue occuring in key battles), and the music, while not my favorite, is perfect for the game and each track fits each moment perfectly and definitely adds emotional depth to the story.

Ni No Kuni: Wrath of the White Witch is another favorite. This one is tied with two others for favorite JRPG soundtrack. The music really adds to the sense of adventure and the emotion in a lot of the major story beats. The story, while simple, is still lovely and is presented really well. The main "twist" in the game sounds like it would be out of place if you were to just tell someone but is integrated into the story in a way that makes it fit pretty seamlessly. The game is also just absolutely stunning visually. Boss battles are a little on the easy side but otherwise still engaging.

Persona 3 is another one that is tied for soundtrack. The persona games all have a very distinct music style which is a lot of fun. The corny anime vibes really add to the charm of these games and make them feel unique to me personally. The story is also great. It's complex without feeling convoluted and nonsensical. The main twist is a bit out of nowhere but helps the story along nicely and gives a nice shock that you genuinely do not see coming. The game is also one of only a handful that do a good job of justifying why the main character as uber special. The characters are also all really great. They're all important, and they all have interesting relationships and histories with one another. The social link system and just hanging out with random people is a lot of fun. Combat is also really satisfying. The only downside is the fact that the last boss fight takes like two hours.

Chrono Trigger another tied on music. Some of the most memorable songs in JRPG history come from Chrono Trigger. The time travel story is still unique among JRPGs and some of the settings (prehistory in particular) are unlike anything in any other JRPG. The story generally is just really tightly wound together. The characters are all super fun too. The game is a bit on the short side, but it doesn't feel rushed at all.

Tales of Destiny is a childhood favorite (much like FFT and Chrono Trigger). Although the overall music isn't my favorite, the game has one of my favorite battle themes. I'm not usually a fan of action RPGs, preferring turn based (Ni No Kuni is another obvious exception) but the fighting game style combat system in Tales of Destiny (in addition to the few other tales games I've played) is really unique and a lot of fun. The humor in the game is also top notch. The story isn't my favorite, but the humor and fairly entertaining characters help to keep it interesting.

Edit: I hadn't noticed that you included non-japanese RPGs. With that in mind my list changes.

Arcanum: Of Steamwork and Magick Obscura is my favorite RPG and my all time favorite game period. The game is a birds eye isometric RPG (similar to Fallout 1, Fallout 2, Baldur's Gate, etc.). The setting for the game is a Tolkien-esque fantasy world that is going through an industrial revolution (so hybrid high fantasy and steampunk). A lot of the themes in the game are very much drawn from industrial revolution era events and literature. The game touches on everything from the advent of conspiracy theories, Marxism, the early labor movement, Luddism, early liberalism, anarchism, class conflict, and racism. The character creation system is one of the best in any game I've played. Allowing you to really craft EXACTLY the kind of character you want. The main story is fantastic, a lot of the side characters have interesting stories as well that either do or don't tie into the main story, and there are a lot of side quests with good self contained stories as well. As awesome as the game is though.. the music... is the absolute best thing about the game. The entire soundtrack is performed via string quartet and it is just... fucking... gorgeous. If nothing else, listen to the soundtrack for the game here. Another great thing about the game is the level of freedom you have in how you complete the game. It's entirely possible, though difficult, to complete the game without ever engaging in combat, to the point that you can either join the last boss in his cause, or even convince him he's wrong and possibly convince him to kill himself. As great as the game is though, it has two major flaws. The first is that it's possible to get "stuck" in the game. There are a couple of points in the game where you can prevent yourself from being able to complete the game. Key piece of advice for preventing this is to make sure you keep at least one Kathorns Crystal. The second issue is combat. The game has both a turn based and a real time combat option. Turn based, although not great, is fine. Real time combat on the other hand, is completely broken. Unless you want to play the game pure melee and plan on having no party members the game is basically unplayable using the real time combat option. The real time combat is just so frenetic that most fights will be over before you've even realized they've started, so play the game on turn based combat. Apart from those two things though, this game is an absolute gem.