How "modern" are we talking here?
Lost Odyssey on the Xbox 360 has received a lot of praise, I've never played it myself but it's apparently very similar to older Final Fantasy titles, and if that's true then I would personally say it's probably worth checking out.
There are a lot of relatively odd JRPGs these days, but they're of varying quality and people will give you wildly varying answers. For instance, I'd personally say Resonance of Fate is worth checking out (it's for PS3 or 360), because it has a highly interesting world and unique combat mechanics, but those same combat mechanics are a large part of the reason why many other people would say "No, you should avoid it".
Then of course there are titles like Folklore or White Knight Chronicles II on the PS3. The former has, again, a very interesting world and some pretty neat pseudo-monster-collection action-RPG combat, while the latter is something similar to Dragon Age: Origins but more generic in world-building and more JRPG-weird in everything else (in particular, its combat can be quite slow and it doesn't have the most gripping storyline ever told).
And the Wii has titles like Xenoblade Chronicles (again fairly similar to Dragon Age: Origins, but with a more open world and far better melee combat) and Pandora's Tower (an action-RPG with a highly strange world and story). I think there's a Fire Emblem game on the Wii as well (Fire Emblem being a series of tactical JRPGs which are widely known for how difficult and punishing they can be, not terribly unlike X-COM).
And then there are even more niche titles like Disgaea or the Atelier franchise, which feature "anime" tropes even more heavily than all of the previous games I've mentioned.
Now, if you had a 3DS, that system has quite a few quality JRPGs on it right now. But... well, yeah. Unfortunately the PC doesn't have much in the way of quality JRPGs right now, there are a few really niche lower-budget titles, but the "creme de la creme" so to speak are basically just the re-releases of Final Fantasy VII and VIII, and... well, those aren't games which have aged particularly well, though I still like them quite a lot.
Oh, there's also Kingdom Hearts 1.5 Remix and soon to be 2.5 Remix on the PS3. They're action-RPGs which combine Final Fantasy characters (and plotting) with Disney worlds and characters. The story is incredibly weird, especially after the first game which has a mostly self-contained plot, and the writing/dialogue can get very melodramatic (I'd be interested in finding out how many times the words "heart" and "darkness" are used throughout the franchise), but gorram I love it too much anyway.