When you play in Career mode you will challenge the 5 Kings (Showdown, Drift, Drag, Speed and Grip), when you beat them you will unlock their car.

Unlock 1965 Pontiac GTO (Nate Denver):
Beat Speed King in Career mode.

Unlock 1995 RX-7 (Aki Kimura):
Beat Drift King in Career mode.

Unlock 2006 Mustang GT (Karol Monroe):
Beat Drag King in Career mode.

Unlock 2008 Evo X (Ryo Watanabe):
Beat Showdown King in Career mode.

Unlock 2008 M3 E92 (Ray Krieger):
Beat Grip King in Career mode.