How can we avoid capital gains taxes on real estate sales?

It's first crucial to determine what kind of property you are selling. The rules are very different for the different types.

Primary Personal Residences
Up to $250,000 per person ($500,000 per couple) of profit on the sale of a primary personal residence can be earned tax free.

Other Real Estate
Gains from sales of second homes, rental, business, farm & investment properties can be deferred (possibly forever) by use of the 1031 (a.k.a. Starker) exchange where replacement property is acquired within 180 days after the original property is disposed of.