In Dark Souls for the PS3 and Xbox 360, you can unlock New Game+ mode to play through the game again with all of your collected items and souls, minus any unique items like keys and such. Note that on New Game+, enemies have almost twice as much health and attack power as your first time playing.
To unlock New Game+, you just need to beat the game at least once. It will display on the screen after you beat the game that you have unlocked New Game+, so make sure to save after that point.
