There are only two games I can really say for sure, since they both keep real-time records. World of Warcraft comes in at number two, with 433 days, 22 hours, 34 minutes, 54 seconds. Number 1, by a frankly unbeatable margin is Realmsmud, a text based RPG made back in 1991, that I played from high school on...that character has (no joke) 2700 days, 11 hours, 27 minutes, played time.
Darth Mornelithe Dark Lord of the Sith
Name : Mornelithe Race : half_troll
Gender: Male Age : 2700 d 11 h 27 m
Class : monk Level : 99
Class2: priest Level2: 76
He is logged on. Idle: 0