Steve McQueen is House's pet rat
Steve McQueen used to be a resident of Stacy Warner's home. In order to try to impress Stacy, House hunted him in her home. However, when House found the rat, he found that he appeared to be ill - he noted that Steve McQueen was turning his head to the side, which is not a usual behavior for a rat (see photo). Instead of killing him, House named the rat and eventually captured, then treated him.
When House brought Steve McQueen to the hospital for treatment, Wilson was at first shocked and feared for the health of the patients. However, House quite quickly pointed out that any disease that is contagious to rats isn't passed on to humans. Eventually, after Wilson moved in with House, he became attached to Steve McQueen as well. In fact, when House decided to use Steve McQueen as a guinea pig when Foreman became sick in Euphoria (Part 2), Wilson was aghast and asked House why he couldn't use a lab rat. House said he needed a rat he was sure was healthy. Luckily, Steve McQueen survived the exposure to what affected Foreman.
Several years later, House referenced Steve McQueen in a discussion about a patient with early-onset Alzheimer's Disease, saying he enjoyed a more fulfilling relationship with Steve McQueen than the patient did with his wife.
The show's producers have confirmed that Steven McQueen is deceased, presumably due to old age as rats seldom live longer than 3 years.