Good info from aesmith .............. as a side note, the distance from the electric fence isn't such a concern. You could be a mile away etc, and still suffer the adverse affects of a poorly maintained electric fence. Grass growing and touching the actual fence can cause the 'Clicking' noise you can hear on the landline, amongst other reasons.
Interference may also occur from poorly designed and maintained electric fences. This type of interference is usually caused by mains operated electric fences which produce high voltage pulses on the fence wires (up to 8kV). The interference is easily identifiable whilst listening on the affected cables. It is heard as sharp clicks occurring approximately once per second, or as periodic lines on fax print outs. Electric fences are also able to affect some types of data service in some way, though broadband has been proven to be fairly immune to directly coupled fence noise, but not very good when the fence radiates noise in the RF region, e.g. when the fences sparks across insulators, vegetation or even joints in the wire.