The turn based combat system was originally invented for video games as a way to easily manage combat situations within RPG and RTS style games when computers didn't really have the processing power to handle the battles in real time.
However that has now changed. Today's computers and consoles can easily process a battle, no matter how large, in real time. However this introduces a lot of problems in itself for the player. In a turn based system the player can easily micro manage each aspect of the battle for each turn without having to worry about something happening during the selection of their next actions. In contrast, with a real-time battle system everything is constantly happening and you do not have the time to consider possible next moves.
Each has something going for it though. With Turn Based combat you can really play around with everything available and experiment, creating routines in certain battles, and then watch them being played out. Whereas in real-time combat you get the sense of being a part of the action, with your adrenaline level increasing as the combat intensifies, giving you a sense of being there.
Different people prefer one or the other. There is also a third system which is a hybrid of the two. Real-time combat that can be paused to manage your characters, then unpaused to continue. Games such as Baldur's Game and Dungeon Siege use this style of combat system and I like this the most. Being able to fight in real-time, but when everything is getting too much, or you lose track of certain events within a battle you can kill the space bar, pausing the action, and then take a few moments to move around the battle and analyse things, selecting the next actions for your characters, then unpausing and continuing with the selected actions played out.
And more games are using this real-time with pause style of combat these days. Fallout 3 is a good example of one of the latest games to do this, with you being able to pause time to select and taget areas of an enemy, before unpausing and watching your weapon's ammo hit home.
So which combat system do you prefer? And why?