My favorite video game...I'll have to go with the one I've replayed the most, which is The Legend of Dragoon.  The storyline and music easily drew me in, but the thing that really kicked it off for me was the combat.  While it was a turn-based RPG, it was the first game I had played that implemented a much more interesting way to fight.  Essentially, your characters are given different move sets, which can be equipped outside of battle, and each one has a different number of additions, or button presses.  Each move set has five levels that increase with 20 full completions of the move, increasing the damage and spirit gained from each hit.

The additions also had to be timed.  Think Guitar Hero, but a square is sitting over the enemy while another spins in from the border of the screen towards that one.  Each move set has a different sequence (though the button to hit was always X), and any move set with three or more additions gave the enemy a chance to hit you with a counter.  Imagine three quick button hits out of seven and the second one suddenly changes, setting off an animation whether you get it right or not.  It throws you off completely, and it made me fight harder to beat the game than I ever had on any other turn-based RPG.  The better your abilities in physical combat, the better your characters are all around (completed sets can give you new ones, and the spirit gain can increase your dragoon levels).

The replays are more or less tests of skill.  Fully training all allies, getting the ultimate armors (crazy expensive), going through the game without using Dragoon powers, and eventually I'll go without dragoons or the ultimate armors.  I just can't keep away from it.