Perhaps the biggest concern you will hear about domestic wind turbine use is that they create too much noise to be used near a home or anywhere near it. In the past this may have been true, but aerodynamics are a lot better understood these days and there are ways to mitigate or virtually eliminate any noise generated by domestic turbines.
Why turbines make noise
When you think about how a turbine might produce noise, you might assume that it's the wind rushing across the blades that's responsible - and this is true to a degree. In some cases, sound is produced by air rushing over the outermost tips of the blades. With certain designs, this produces a high-pitched whining noise in high winds. If the turbine's up high enough though, the sound will barely be audible, and it's quite possible you won't hear it at all. Many modern designs feature enhancements to the blades (including rings added to the blade tips) which remove that source of noise entirely.
The greater source of noise from wind turbines comes from the sound of the generator attached to the rotor. This spins the magnets around the coil to produce electricity, producing a low humming in high winds. This noise is almost always ground-based. If the structure is freestanding, then most of the noise is absorbed into the ground but if it's attached to a building (your home, for example), it may even resonate through the whole structure. This can be a serious nuisance, especially at night when you're trying to sleep.
What can be done to mitigate the noise?
If your turbine must be attached to the house, it may not be possible to entirely eliminate the sound, but adding in some thick rubber mounts will absorb a lot of the transmitted sound and provide a break for the vibrations. The idea is to isolate or decouple the vibrations of the generator as much as possible using materials which will absorb a lot of the resonance. The right sound insulation techniques will go a long way towards reducing the noise.