Buzzing in an AC adapter can mean a number of things, but often it is related to a damaged adapter, poor grounding or phasing issues with your power. Figuring out exactly why your AC adapter is buzzing will probably require some troubleshooting, but in the end you can probably isolate the problem and get rid of the frustrating noise.
Check for any obvious damage to the adapter. If any of the outer rubber coating has been damaged so that the conductor inside is exposed, this could allow interference to enter the current and cause a buzzing sound. Untie any knots if the cord has become knotted. Make sure that the connection where the cord meets the actual box adapter is still intact; this sometimes can become damaged and make a poor connection.
Repair any damage with electrical tape. Cover all exposed areas.
Plug the AC adapter into the same outlet as the other equipment you are using. Some apartments and houses have multiple phases of power that can create audio interference if mixed together, so running everything off of the same phase might get rid of the buzz.
Run your equipment through a surge protecting power strip or, if necessary, a power conditioner. Audio and video equipment is especially susceptible to interference caused by ground looping. A power conditioner will smooth out the current and protect your equipment from any peaks or spikes in current.
The quietest way to run any piece of equipment is with a battery. If the equipment you are attempting to use gives you the option of running it on a battery, this will eliminate the buzz.