Why do rockets spin as they lift off?

Answer 1

They don't, they are gyro stabilized to prevent this.

Answer 2

There are two reasons rockets might spin. In the case of unmanned rockets, the spin is to stabilize the vehicle during its launch through gyroscopic forces. This is to prevent tumbling, which would cause the loss of the rocket and its payload.

Manned rockets or boosters intended to reach orbit normally have a roll program designed to align the vehicle properly to enter its orbital trajectory. Watch a shuttle launch and you will normally observe the roll program in about the first 15 seconds after liftoff. This is an entirely different purpose. These vehicles are stabilized mainly through gymbled thrusters on the rocket booster.

Early rocket launches were often plagued by instability just after launch. Beginning with the German V-2 rockets the vehicle was spun on a turntable prior to launch. These turntables were used in the Army's Redstone and Jupiter missile launch systems. Other large rockets used thrusters to introduce the spin after launch.