I love a good combat system.
One of the best in my opinion is the Paper Mario one, very simple but very involved. Having the right badge set up, right partner, and nailing the timing of your attacks makes for a really interesting system.
Golden Sun is my favourite of the more traditional style ones(beating out Chrono Trigger slightly and classic FF and DQ)
It takes the classic formula of the old games and did some interesting things.
You equip little elemental creatures called Djinn and the mix and amount determines your class(and abilities). But, in battle, each djinn has an ability(like an attack or spell) and once you use one, it will be inactive and no longer contribute to your class(your class may change now as a result of using one, and your stats will be slightly reduced). You can use a turn to reactivate it, OR you can use it to call a summon. This is where it gets interesting, because having a certain amount of these djinn on standby changes what you can summon. Having 4 earth djinn will get you a strong earth summon "Judgment" or in the second game, 1 earth and 1 fire will summon "Zagan".
It may sound complicated but it makes perfect sense as you're introduced to it in-game. Makes for some cool and strategic battles on what appears to be a basic turn based battle system at first.
Blue Dragon on Xbox360 was another good one that shookup the classic formula a bit.
The main interesting thing here for me came from how they managed the turn order. There is a bar which shows the turn order timeline, such as who is next and who is after etc. But some attacks and all magical abilities give you the option to charge them up and this can change your place in the turn order timeline, but it requires good timing much like Paper Mario. Battles become so much more strategic when you are trying to find the most effecient way to kill all the enemies quickly whilst also trying to balance ability strength with turn order. Really cool game.
Now, for something different. Gladius on Xbox, PS2, and GCN.
It had an ancient greek theme which was cool but the battle system is one of my favourites overall. It was a 3D grid based strategy game, along the lines of X-Com and such.
What made this interesting for me was the swing meters. Regular attacks had a swing meter, much like you'd see in a golf game, with the first large section giving you a standard attack, a small critical hit sectuon, and a part at the end that guarantees you missed.
It made the combat feel more skill based than relying on stats and RNG. If you missed, it's because you missed, not because the RNG didn't favour you.
Abilities and magical attacks often had unique inputs too. Combo attacks had a normal attack swing meter with different inputs all across it, or some attacks required mashing A or X, with a few more I forget. But overall it made the battles more exciting and you felt more in control. It was a really great game.
Now these ones are a bit rough and not overly well received games but I still loved them.
Holy Magic Century/Quest 64 and Aiden Chronicles were both N64 games that used the same battle engine(I believe THQ bought the engine from Quest 64). It was mostly turn based and on your turn a circle appeared around you(size based on your stats) and that dictated how far on the battlefield you could move on your turn. The other interesting part is that during enemy attacks(at least in Quest 64), for a moment you can move and attempt to avoid the attack which was usually quite difficult but spells had patterns you could learn.
Lastly, something a bit weirder but really cool.
Hybrid Heaven on N64.
It at first looks like some sort of 3D fighting game on battles, you can run around in real time but you're always facing the single enemy. Where it gets interesting is when you initiate an action, the game pauses and a menu appears. Based on how much stamina you have left, you can choose a variety of kicks and punches and grabs/throws. Even eventually combos.
Now this happens during enemy attacks too, but your options are on attempting to anticipate the enemy attack by blocking, or evading, or if you're feeling confident, countering the attack. The enemy behaves the same as you so they can initiate grabs and combos too and can also attempt to block, evade or counter.
The other cool part about the game was the levelling system. After the battle your body parts would level up based on the battle. Do a lot of right hand punches and your right arm offense will increase. Get punched in the head a lot, head defense will increase. You also learn grabs/throws from having them be used on you. Oh and if I remember correctly, body parts can be damaged in battle from excessive damage so that renders them useless for attacks and can reduce your mobility or defensive options.
Anyway, sorry for the wall of text but I get really passionate about certain battle systems!