Sly Cooper and the Thievius Raccoonus
It is unknown how the van was first obtained, but Murray was very deeply connected to it. It was very useful in Sly Cooper and the Thievius Raccoonus, serving as the Gang's getaway vehicle, as well as being used in races and firing turrets. The Van had a satellite, and in "The Cold Heart of Hate", it gained rooftop turrets to fire at Clockwerk's goons.
Sly 2: Band of Thieves
In Sly 2: Band of Thieves, it's usefulness decreases a little bit, as it is never used in actual gameplay, but it is always ready as the getaway vehicle. At the end of Episode 3: The Predator Awakes, Bentley is forced to learn how to drive the van in order to escape the jungles of India and also to rescue his friends. It is used as the main transportation vehicle until Episode 7: Menace from the North, Eh?, when it is seen floating away on a piece of ice in Canada.
Sly 3: Honor Among Thieves
In Sly 3: Honor Among Thieves, the van is never mentioned until Episode 4: A Cold Alliance, when Penelope reads some strange signals coming from the bay. Reconnaissance showed the disturbance to be the team's long lost van. With the help of both Penelope and the Panda King, Murray is able to haul his van back to the Safe House where Sly and Bentley (with a little help from Carmelita) recharge its batteries for the team's getaway. Later in the game, the core members use the Panda King's fireworks to launch the van up to the Cooper Vault to rescue the Cooper Family fortune. After the Cooper Vault Job, Murray takes the van and begins his career as a racecar driver, Stock-Van class.
Sly Cooper: Thieves in Time
In Thieves in Time, Bentley has converted the van into a Time Machine. The Time Machine was first mentioned in the ending of Sly 3: Honor Among Thieves. Bentley infers that he wants to use the Time Machine to see what their future holds, now that Sly has run off with Carmelita, Murray's joined the racing field, and Bentley and Penelope are the keepers of the improved Cooper Vault and the Thievius Raccoonus.
Between the events of Sly 3 and Thieves in Time, Murray continued his racing career, until he could no longer find a sponsor due to his high insurance premiums. Because of this, Murray headed into the Demolition Derby, where he remained undefeated. He dropped everything when Bentley showed up and informed Murray that the van was an integral part of his (Bentley's) plan to save Sly's family history from being erased forever.
The Time Machine is an integral part of Sly Cooper: Thieves in Time, as it is used to travel back and forward through time to different periods where Sly's ancestors live, the mission being to restore the pages of the Thievius Raccoonus. In Thieves in Time, the Time Machine uses carbon-dating to travel through time, using various artifacts to travel back to the specific time periods, including: Samurai Dagger (Fuedal Japan), a old western Sheriff Badge (Old West), Murray's Australian Fossil Necklace (Ice Age), Grizz's Crown (Medieval England), Gold Coin with a Jewel in the center (Ancient Arabia), and an Eiffel Tower Keychain (to return to the present day). The hover boosters on the improved van also allow it to fly.