One battle system I really liked, but haven't seen mentioned yet, was in Fate/Extra. It does have its shortcomings, like the fact that it only really works for one-on-one fights with maybe a single supporting character on each side, but it is a lot of fun.
It's like the duel system from the Suikoden series, but you input six commands per turn. You can Attack, Guard, or Break; Guard beats Attack, Attack beats Break, Break beats Guard. As you gain familiarity with a type of enemy, you'll be able to predict their attacks more consistently; at first, you'll only be able to see one or maybe two of their actions per turn (and predictably counter them), but once you kill enough enemies of that type, you'll eventually get to see all six of their actions when inputting your own actions.
Boss fights instead require you to research your enemy to get a decent sense of how he fights. No research completed means you only get to see one or two of his six actions each turn, but full research means you see four or five of his actions. Even with a fully researched boss enemy, he'll throw some spells in the mix, which you can't really counter, so boss fights remain challenging.
As a supporting character, you get to throw spells and use items, but these will take the place of your champion's attacks, so you have to be careful.
It's a really fun battle system, if perhaps a bit limited in scope. --- "We have a Constitution to protect us from the rule of 'most reasonable people'." -Butters (not the one from South Park)
I loved FFXIII / FFXIII-2's battle system. In fact, FFXIII-2 was the first (J)RPG in which the random encounters not only didn't bother me, but kept me entertained throughout the entire game. People tend to look down on it, saying it's nothing more than pressing X, but that's nonsense. The challenge doesn't lie in selecting your attacks, but in managing your paradigms. Which starts of easy enough, but once the game has opened up, you'll need to know exactly when to switch and what paradigm to make use of, otherwise you're toast. THe whole monster element added in FFXIII-2 made it even more fun by giving you all kinds of cool creatures to fight besides you. I thought it was gimmicky at first, but I ended up loving it.
I also want to mention both Devil Survivors. The battle system in those games was new, fun and surprisingly deep.
Best? I dunno, but I always liked how Ar Tonelico 3 did it, you fought to the sound of the music. You were on a team with three fighters and 1 support. The music would be different in different situations and slightly different depending on what support you had. As you fought, it was in real time but you had to try and attack on the high notes of the song, which would give the support more power, which would make the spell you would have her cast, be even stronger. It wasn't perfect, but it was an interesting way of doing it and I would love to see other games try to implement something similar.