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Having lived with Sheldon for many years, Leonard knows him better than his other colleagues: this has led Sheldon to believe (slightly erroneously) that Leonard is his best friend.
Nevertheless, Leonard often finds himself explaining Sheldon's behavior or serving as a mediator between him and other people in many situations. For instance, when Penny and Sheldon engaged in a fierce dispute, Leonard gave Penny Sheldon's mother's phone number so she would call her son and scold him for his behavior, thus ending the fight.
"The Staircase Implementation" features a flashback to when Leonard first moved in with Sheldon. Leonard explains to Penny that he moved in despite the difficulty of living with Sheldon because the rent was so reasonable. Shortly after moving in, during a rocketry experiment Leonard, Raj and Howard conducted, Sheldon observed miscalculations Leonard made in mixing the rocket fuel and managed to avert disaster by grabbing the fuel and placing it in their apartment building's elevator. The resulting explosion disabled the elevator, thus explaining why the elevator is out of order for the duration of the series. Leonard explains that Sheldon, despite his tendency to alienate others, kept quiet about Leonard's destruction of the elevator. (Leonard cites: "He didn't rat me out to the building manager, or the police.... or Homeland Security.")
Source: Wikipedia.org