Done right, ventilation can lead to quite significant gains in energy efficiency. If there is no excess heat gain through windows or infiltration, air conditioners don’t have to work as hard to maintain a cooler temperature. Done wrong though, ventilation can lead to increased electricity bills.
Of course, natural ventilation options will give you some air movement in your home, however because wind ventilation and stack ventilation methods rely completely on nature, they're often not as effective or reliable as powered systems. Powered systems, however, inevitably involve added running costs which mount up as time goes by. Having said that, effective natural ventilation and mechanical ventilation are both cheaper to run than an air conditioner when done right - and if you're also on solar power, it's likely that it will only slightly factor into your overall energy usage.
Mixed mode ventilation (also known as hybrid ventilation) allows you to take advantage of both natural and mechanical ventilation methods. Automated mixed mode ventilation systems can be set up to use natural ventilation when conditions are good enough to allow it, and then automatically switch over to mechanical ventilation whenever it's needed. This type of system requires extensive programming, various monitoring sensors and automation controls, but once it's up and running it's a very cost effective and energy efficient way to carefully control over your home's ventilation.
A whole-house fan is another very efficient method of ventilating your home. These are especially useful in areas where humidity levels aren't too high. In fact, according to the US Department of Energy, replacing an air conditioner with a whole-house fan can potentially correspond to a saving of up to 30% in cooling costs. Because they can provide up to 60 air changes per hour throughout the entire house, these types of systems are very effective for ventilating an entire house.