For me, personally, it's impossible to separate the core battle mechanics from the encounter design and difficulty, which is where a wast majority of JRPGs fail. Pokemon, for instance, might have an amazing system for multiplayer battles, but when every singleplayer fight can easily be won by using one ability over and over again, none of the things that make the game popular in multiplayer are ever given a chance to actually present themselves to the player. The same can be said for many other JRPGs. I never understood why people say Final Fantasy X is great, for example, when most normal fights in the 10 or so hours I've played it could be won with just normal attacks.
Some games I personally feel do it right would be:
Turn Based: Trails in the Sky trilogy
A pretty standard turn based JRPG system with an addition of light positioning and the ability to manipulate the turn order. Probably the best "traditional" JRPG combat system, since the games (particularly the last one in the trilogy) are great at providing varied combat scenarios that force you to actually experiment with different team compositions. While the second game can feel very unbalanced at times, I was actually incredibly surprised at the the final game in the trilogy (the 3rd), where increasing the difficulty not only ups the enemy stats, but also changes combat encounters with different enemies/abilities. It's a shame the same can't be said for the Cold Steel games, which are incredibly easy even on their hardest difficulty setting.
Strategy RPG: Growlanser IV
This is probably the best example of how good mission design can vastly improve the game. The mechanics of the combat system are pretty simple, since you'll mostly be using just two commands (move and attack). But the missions elevate the game's combat to probably my favorite combat system in any SRPG. Most missions will give you an objective that is different from just killing everything, or will put some special twist you have to be aware of. Some missions also feature difficult bonus objectives that sometimes change the outcome of the story. In addition, the game is hard enough that positioning of your units is incredibly important, and most missions are designed in a way that will force you to figure out how to optimally split your forces. The same team later went on to make the SMT: Devil Survivor games, which are also incredible SRPGs, even if they lack a bit in terms of mission variety.
Action RPG: Ys series, in particular Ys Origin
Unconventional Combat Systems:
I really love it when a JRPG tries something different and original with its combat system. Some of the games that I enjoyed that did that would be:
Baten Kaitos Origins
Knights in the Nightmare, a real time strategy bullet hell RPG, where the player character is essentially a cursor that needs to dodge enemy attacks while at the same time issue orders to the units under your control.
The World Ends With You
I really liked the whole controlling two characters at the same time thing. The game also lets you customize the difficulty, and even delevel yourself if you find the game to easy, which is something I wish more JRPGs would include, since most of them are much too easy.
. Not just that but the intersection between the Brave/Default system and the Job system gives you a very large amount of flexibility.