Front sway bars are a strict necessity for any vehicle's suspension, but rear sway bars are more important on some vehicles than others. How important they are depends on the application.
Sway bars are torsional springs that connect the wheels on either side to each other and the chassis. Removing a rear sway bar increases the amount of rear body roll and tendency toward over-steering.
Because all front wheel drive (FWD) cars have a natural tendency to under-steer while on power, removing the rear sway bar can actually help during performance driving. It will, however, make the back more prone to sliding when cornering.
Removing a rear sway bar on a Rear Wheel Drive (RWD) car will make it prone to over-steering off throttle and power-sliding (drifting) while cornering under power.
Four Wheel Drive (4WD) and all wheel Drive (AWD) vehicles are affected by sway bar removal in much the same way as FWD cars.
Back-heavy station wagons, SUVs and hatchbacks will exhibit much more body roll and over-steer with the rear sway bar removed. Pick-up trucks will develop a tendency to power-slide.
