In general I would recommend to spay or neuter between 5 or 6 months.  This recommendation may vary based on each individual pet and the specific issues that may be of concern.

I recommend spaying dogs and cats before their first heat cycle.  This greatly reduces their chance of mammary cancer later in life.  One exception may be in giant breed dogs, as by spaying them prior to their first heat cycle may  reduce their overall growth, however the risk of mammary cancer still is an issue.  These issues and pros and cons should be discussed with your veterinarian on an individual basis.

As for males I also feel six months is ideal, but this should be discussed on an individual basis.