I live in the humid deep south. It can be done, but not all structures lend themselves to it. Most of the houses I lived in AC free were of the older design and for the most part were at least partly shaded by large trees. No AC and only fans will save money. You can save some by using a window unit only in the bedroom when sleeping. I have done that in the past. The other thing I do is put ceiling fans in every room. Keeping air moving is the key to staying cooler. I would also take a shower right before bedtime and sleep in front of a fan, some people can't stand to have the fan blowing directly on them.

Aaron