Dean's car, affectionately dubbed the "Metallicar" by fans, originally belonged to John (see 1.01 Pilot, where John sits with his children on the hood of the car while his house burns, and 1.20 Dead Man's Blood, when John mentions that he gave the car to Dean).
The nickname "Metallicar" originated on the fanboard Television Without Pity. The actual comment where the term was first used by Cyb is on this thread on October 11, 2005. It was coined because Dean enjoys listening to classic rock music like Black Sabbath, Led Zeppelin and, of course, Metallica while driving.
Until mid-2007, Television Without Pity in association with Glarkware, produced "Now or Never" t-shirts, which were available only for one month. The tees often featured phrases coined by fans on the forums. Their Metallicar tee in 2006 was one of the most popular. In May 2007, a version of this t-shirt was once again offered for sale for a limited time.
In November 2007, a t-shirt offered by Power Star Collectibles featured a picture of the Impala with the caption "Metallicar" - an indication that the term had entered a broader domain.
Eric Kripke mentioned that he knew that "fans online" referred to the Impala as "Metallicar" in the commentary on 2.21 All Hell Breaks Loose: Part OneS2DVD and also in the first issue of the Supernatural: Official Magazine.