First, keep in mind that I'm not a fan of the "standard" JRPG. By "standard" I mean cutscene-laden, super-easy, childish-story-that-takes-itself-too-seriously JRPGs. That said, my favorites on the PS2 were/are:
Shin Megami Tensei Nocturne: A deep, immersive, and challenging dungeon crawler. Everything about this game, from the Pokemon-like creature maintenance, to the turn-based battles that require actual strategy, to the unique setting and characters that are about as far from cliche as you can get, is just superb. It's expensive on the secondary market, but I cannot recommend it enough.
Shin Megami Tensei: Persona 3 FES: I'm about 15 hours into it right now. It's basically "Nocturne-lite plus high school," and it somehow works. The battles aren't as satisfying because you only control your main character (don't let that discourage you, though, as your party members have excellent AI, and you can control their AI setting on the fly), and the setting, story, and characterization aren't quite as dark as Nocturne, but the creation/fusion system, social links, respectable difficulty, and "just-one-more-turn" progression will likely keep you playing for all of the main game's 70 hour length. Oh, and there's also a second campaign that's supposedly another 30 hours or so. That, and it's only $30. New.
Shin Megami Tensei: Digital Devil Saga 1 & 2: By now you should be seeing a pattern. I love Atlus for developing what are basically JRPGs for adults - both in story/setting and challenge level. The DDS games aren't as good as the first two because they lack the innovative fusion system, but they'll give you your dungeon crawler fix just fine.
Shadow Hearts 1 & 2: I'm grouping these together because they basically tell one continuous story. These games lean toward the easy side of things, but what sets them apart is the inventive "judgment ring" battle system, which makes for a hybrid turn-based/twitch-based gameplay experience. The setting is also a nice change from your usual "generic fantasy land;" both games take place in an alternate early-20th-century Earth where magic and demons exist. Oh, also, you should know that these two games are actually funny. No, scratch that: not just funny, but hilarious. Most games that attempt humor tend to fail miserably, but these are two of the few that succeed. [Give From the New World a miss, though; it's awful in comparison to the first two.]
Dragon Quest 8: The penultimate "oldschool-style" RPG. You walk around, you grab treasure, you kill things in long dungeon treks, you level up, and sometimes you make stuff in your alchemy pot. And that's about it. And, really, that's all you need when a game like that is as polished as this one. The story is mostly fluff, and that's all right by me.
I've tried a bunch of others - the Xenosagas, Star Ocean 3, all of the Final Fantasies, Kingdom Hearts, and so on - and they've ranged the gamut from, "okay but not worth the time commitment" to, "ugh, why did I buy this?" So, if you have any questions about any of those other games, please say so. The seven that I've listed above are the only ones I consider essential buys, though.
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom
