NZ doesn't, but the US definitely does which is infuriating when you're considering moving to a country with a top rate of 33% and no capital gains tax! Also, there is a tax treaty between the two countries to prevent double taxation and the US exempts up to ~$100k of foreign-earned income I believe, but if you're a high earner or make serious profit on property and/or stocks you could find yourself writing a big check to the IRS to make up the difference (not to mention the hassle of filing taxes each year).
Yeah, it's a pain. I left NZ right when my salary was crossing the foreign earned income exemption limit. I never had to invoke the tax treaty and don't even believe TurboTax has an option for that. Would have needed to hire a tax consultant most likely.