I was addicted to Final Fantasy VII way back when; I played it every day, non-stop until I beat it. I was so enthralled by the game that I actually remember skipping food, shower, and sleep at least once. Good times.
The other game I remember being addicted to in recent years has to be Mario Kart DS. It was my very first experience playing online, so I remember playing Wi-Fi matches constantly every day, from dusk until dawn. Matter of fact, I played the game so much that one of the hinges of my first Nintendo DS Lite broke, and the control pad and ‘A’, 'B', and ‘R’ buttons are stuck. The DS still works, though, but all I can play are stylus-based games on it.
My main addiction when it comes to games, although for me is more of an obsession, has to be Pokémon. My life was changed ever since playing Red Version.