Good fences may make good neighbors, but how high can your fence be? In Los Angeles the answer is not so simple, and depends on the location of the property.

In most residential zones (R1 zones), the front yard fence can be 3.5 feet high, and the side and rear yard fences 8 feet high–if the width of the lot is 40 feet or greater ( 6 feet if less than 40 feet). In some cases, an 8-foot fence can be installed in the front yard–with the permission of the Department of City Planning. 
Keep in mind that while the side yard fences can be six or eight feet tall,  they can only be 3.5 feet tall from the front property line to the required front setback line (usually the front wall of the house).

Other zones have different regulations. Properties in the RA and A zones can have a front yard fence that is 6 feet high. In Hillside areas (determined by the City, not by the actual flatness of your property), fence heights vary, and you must consult with an architect or building official to get the information for your specific lot. Wood fences typically do not require a building permit, but masonry fences do, when they’re taller than 3.5 feet.

In Hillside areas, if you want to exceed the allowable building height, the application process frequently requires public hearings.  But with fences, you can avoid public hearings by submitting the neighbors’ written approval with the application.

Other cities in the area have different requirements. In all cases it is best to visit the local building department and ask a building official.

Resources.
The Department of Building and Safety’s handout.
Beverly Hills fence information.