Well some tire manufacturers recommend getting your tires balanced every 3,000 - 6,000 miles but that is really too often.
That is mostly to make tire shops money because they make money every time they balance your tires.
Most people drive 12,000 miles per year and never balance the tires on the vehicle and nothing bad happens.
I personally never have my tires balanced except for when the new tires are installed.
If you don't have your tires balanced when the tires are mounted on the rims the tires could cause vibration in your vehicle and shake your steering wheel as well.
I was once driving my truck and a wheel weight fell off causing my steering wheel to shake so bad that the bolts holding my steering column together under the dash vibrated out.
Luckily I was driving down a slower road and was able to pull over and get those bolts back in.
Really though you never really need to have your tires balanced unless you experience shaking or other issues with your vehicle.