The guys have introduced it sometime before the episode "The Hofstadter Isotope" (S02E20) to have a little change in their routine; however, Sheldon struggles to cope with it, in particular with his digestive system. The others guys wanted to visit a bar to look for women; however, they end up at the comic book store which is normally a Wednesday activity.
In "The Anything Can Happen Recurrence" (S07E21), it is revealed that the guys stopped doing "Anything Can Happen Thursday" because Penny made fun of them and said it was stupid. When Sheldon needs to take a break from finding his next area of focus in science after giving up string theory, Leonard suggests to bring "Anything Can Happen Thursday" back and Sheldon agrees. When Sheldon, Leonard and Penny cannot think of anything to do, they just leave the apartment for a walk to look for a new restaurant. Penny ends up taking Sheldon to a psychic.