Tax Analysts has a small article about U.S. baby boomers retiring outside the U.S. There are some tax benefits (relatively small, usually) that are highlighted in the article.
In our practice we see some of this. The tax angles are usually secondary to the clients we work with who move out of the U.S. After all, as long as they maintain U.S. citizenship they are taxable on their worldwide income. (One benefit, though, is that they get away from State income taxation). But usually the key motivating factor is the ability to buy a lot of lifestyle at the same amount of money.
We rarely see people willing to give up citizenship (or legal permanent resident status) simply to avoid the U.S. tax bite. In fact, I had that very conversation with someone last week. The tax benefits are simply not enough to justify foreclosing all of the benefits of having the U.S. passport or green card.
For the few who want to do this, we walk them through the process and structure their financial affairs to minimize or eliminate U.S. tax bites after they give up their passport/green card and leave the country.
In that sense, giving up citizenship to save taxes is a lot like asset protection trusts–far more frequently talked about than done.
More common–for our tax advisory practice, anyway–is the U.S. business executive who moves abroad for a period of time, intending to return after a few years.