The wheel spacer essentially changes the offset of the wheel you are using it with.
If you use them with stock rims you will essentially push the centerlineof the wheels out. This will put more stress on the wheel studs, bearings and also the rubber bushings in the suspension components. The bigger the wheel spacer, the more effect. Also, torque steer will increase as will squirminess under braking due to the increased track width and subsequent deflection in suspension components.
You are changing the axis that the rubber tire rotates around when the wheel is turned. It is technically called the "scrub radius". The car is set up with a specific scrub radius geometry and departure from that will cause adverse effects. This is why there is talk of getting the correct offset in a rim. (it's not just because people will "rub" when they "slam it").
If you use a wider wheel it doesn'y necessarily make any difference. What makes the difference is the offset you use. you can have a 9" wide wheel with the correct offset and the scrub radius will be zero (disregard that suspension components may be in the way with this example).
Spacers are used to "fix" a rim's offset. If the rim is made with too much offset the spacer is used to push it back to where it should be. If money was not an issue you'd just have the rim made with that specific offset and not bother with spacers.