The late 80s Honda Prelude and Mazda 626 (European names, of course, the American counterparts may be named differently) both had versions with 4WS (Four Wheel Steering). At high speeds, the rear wheels would steer in the same direction as the front wheels, causing the car to switch lanes more gently. At lower speeds (say, parking), the rear wheels would steer in the opposite direction, thereby increasing the manoeuverability of the car in small spaces.
While this facilitated parallel parking, it by no means meant that the car could just slide in laterally. A system like that requires the wheels to be able to twist completely sideways. Some off road vehicles have that possibility, but it requires a lot of space and it is expensive to make and maintain.
Here’s some more background on the technical history of 4WS, and why it’s not being used anymore today.
Incidently, my car (peugeot 306) has an active self-steering rear axle that makes it really fast through corners. Doesn’t do anything for parking agility though.