*cracks neck*
Chrono Trigger (SNES/DS): This is THE most perfect oldschool JRPG ever made. It's got a good plot with memorable characters, a fun combat system, and it's just all around a ton of fun. If you can get the DS "remastered" version, get that one. The translation job is MASSIVELY improved, no matter how much the purists miss "ye olde english" speaking Frog.
Essentially, it's a story about a trio of teens living in a pseudo-post-medievalish world who accidentally discover time travel, and find out that their world will end in a horrible disaster in about a thousand years. So, for lack of anything better to do, they set out to change the future by traveling to several other time periods to discover a solution.
The World Ends With You (DS): A JRPG that feels totally unique and fresh. It's got a modern setting, a battle system that's not turn based at all, and is incredibly tricky to master, but so much fun that you will seek out battles just for entertainment.
Basic premise is that the main characters are paired up in a sort of supernaturally-twisted version of Shibuya, and need to accomplish specific missions each day or they'll be erased from existence. And just when you think "Man, this game is
insanely short", BAM, you realize you're just at the beginning...
It's up there sharing the top spot on my "best RPGs ever" list with Chrono Trigger. Both games are incredibly wonderful and you really should play them.
The "Etrian Oddyssey" series: (DS/3DS)
It's a first person dungeon crawler series, where you create your own party of 5 explorers of various classes, and you explore a giant labyrinth, literally drawing your own map on the bottom screen. It's also BRUTAL. Almost every floor has at least one miniboss, often MANY (called F.O.E.s), which patrol specific routes and if they catch you, they will probably utterly destroy you because they're magnitudes stronger than anything you'll find in that general area.
So you explore, you kill monsters, bring their parts back to town, sell them for money (and to unlock new gear in the shop), so you can go deeper into the maze and find new shortcuts so you can eventually make it to the next boss as fresh as possible. It's a fantastic series. I'd recommend starting with EO4 on the 3DS, since it's the most accessible of the bunch. And then if you somehow can, pick up the 3rd game. That one had the best damn story in the series, I tell you.
Xenoblade chronicles (Wii) is fantastic as well. If it wasn't for the fact that it drags on a liiiitle too long at the very end, and the fact that the difficulty ramps up suddenly at the end, with next to no sidequests left to help yourself level up right near the end, this would be my favourite JRPG of all time. It's amazing. Get it.
And if you're looking for more crazy-hard RPGS:
Anything in the Shin Megami Tensai series, by Atlus. It's the same publisher as the EO series mentioned above, but the SMT series does NOT hold any punches back. It WILL crush you mercilessly and frequently unless you know what you're doing.
The Persona sub-series of the SMT games are a bit less harsh and are definitely worth playing (Persona 4 was fantastic, IMO) as well.
And I'd like to recommend one of my own RPGs, or several RPGmaker games made by some people I know are good at it...but I can't link to them in a topic, that feels too much like advertizing. Lemme know if you want links via PM.