The Press Turn system is my favourite by far. The SMT games are some of the few RPGs I can think of where stat buffs and debuffs can make or break a battle. The way you can gain or lose turns for exploiting weaknesses or hitting resistances (and the way this applies to the enemies as well) adds tons of strategies to each battle. You need to be tagging in demons who resist an enemy's main element, keeping your PC's resistances relevant to the area you're in, casting the right spells at the right time and making sure your party is aligned in optimal order to maintain turn efficiency. The battles are incredibly quick and strategic skill will be the difference between taking out an enemy without taking a scratch and a total party wipe.
The high speed of the animations in the games makes everything feel powerful, too. Annihilating everything on screen with maragidyne feels way meatier than doing the same with firaga in the 3D Final Fantasy games because it just makes everything instantly EXPLODE (imo, at least).
The Grandia system is great as well. Sort of similar to the ATB system in that there's a real time gauge determining turn order, except there's one gauge for everyone and how fast you progress up it depends on your stats. Unlike the ATB system, the game pauses completely to let you make choices, and this is very important as, again, unlike ATB you can interrupt attacks. Hitting somebody will cause their icon on the turn gauge to stop for a while and if you pull off a fast move whilst they're casting a slow, but powerful one? The move will be cancelled and they'll be knocked back to the start of the gauge. On top of that, your actions will change where your character is located on the battle screen, so you need to consider positioning, too. Hitting an enemy on the other side of the screen takes longer than one that's next to you, risking interruption. This makes it very important to watch the gauge as your moves might be interrupted too. If the enemy's turn is close to yours and you're fairly close to them, maybe a slow, lumbering move is a bad idea? On the other hand if their turn is slightly ahead, maybe they've been charging up, maybe this will be a good opportunity to interrupt?
Final Fantasy X has a pretty cool system, too. I was glad they ditched the ATB system; it wasn't bad (I especially liked it in IV and V) but it was never my favourite. Being able to see the turn order and how your actions will influence it makes you consider your tactics a lot more. Delaying enemy turns is much more important than in any previous games (where it was only really possible by using Slow or Stop, IIRC) and being able to swap out your characters and equipment to suit the situation prevents anyone or anything from becoming truly useless. It allows for some interesting tactics, too. If someone is badly wounded, but your healer won't get a turn until after the enemy, you can simply swap them out for someone in good health for now.
Spiderweb Software's games have some pretty cool combat. Not "the best" but I feel they're kinda unnapreciated and worth mentioning. They're grid-based, with turns based on initiative rather than "team" turns (like D&D or the above-mention Final Fantasy X) and what you are capable of doing is determined by action points (like Fallout 1 and 2). Most of the games have a system similar to D&D's "attack of opportunity" where, if you're adjacent to an enemy and try to move away, they get a free attempt to attack. But in Spiderweb games you are, instead, "slowed", so you don't take damage but you can't move as far. It really makes you consider who to send out to the front lines. The battles are very fast-paced, not very flashy, but very satisfying. The action-points system forces you to think hard about what you'll do in a turn. You can use it all on moving or you *might* be able to heal then attack if you're lucky.
There are too many I could mention, Final Fantasy Tactics and V, Tactics Ogre, Xcom, SMT: Strange Journey (which doesn't use press turns), Persona 3 and 4 (which use a variation on press turns, called "one more!", though they do get repetitive due to the calendar system slowing your progress through the dungeons), Temple of Elemental Evil (the best digital implementation of D&D rules ever, for my money). I really love turn-based combat.
I've been meaning to pick up Jagged Alliance 2, can anyone confirm how good it is? I wasn't *too* keen on Silent Storm if it helps, but that was mainly because having snipers made it too easy.