The first of these is Breath of Fire 4 for the Playstation. At the beginning of every turn, the player picks three characters out of the six available, and gives them commands. Those three characters move up to the front row of the battle to fight, while the other three characters move to the back row and sit the turn out. Moreover, the three attacking characters will act in the order in which they were selected. So, if the player orders Ryu to attack, Nina to blast with a fire spell, and Cray to use a status spell, they will carry out those actions in that exact order.
Yet, speed is still an important stat in the game. Nina is incredibly fast, easily capable of moving before any enemy does. Ryu is a fair bit slower than Nina. Cray is very slow, and will generally move after the enemies. So, if the inputed order is Nina, Ryu, Cray, then Nina will move first, before the monsters do, while Cray will move last. However, if the action order is reversed, making it Cray, Ryu, Nina, then Nina and Ryu will wait until Cray takes his turn, with the monsters most certainly acting before he does.
The Playstation 2 RPG Wild ARMs 3 had a nearly identical system. The four party members acted in a very specific order based on their speed stats (typically Virginia, then Jet, then Gallows, then finally Clive). However, the player could manually change the action order into whatever he wanted during a battle. So the player could have Clive move first if he wanted, though typically at the cost of letting the monsters get the first action.
So, it was possible in both of these games to intentionally let the monsters go before the heroes do, or to hold back the action of a powerful attacker until a slower character could cast a buffing spell. Not only is there no chance that the turn won't play out the way the player expects, but the action order becomes a tool the player can use to create more complex strategies. Arguably, this system gives the player even more control over the flow of battle than the Final Fantasy series' Active Time Battle system, where a character has to forego acting in order to letting other characters move first, which is a net loss in the number of actions the team can take.
Hmm... Maybe I should talk about other RPG action systems sometime.