From how I understand it, when you decide to exercise your options (pay the strike price), you owe taxes on the different between your strike price and current fair market value even if you don't sell the stock. Most of the time, this counts as AMT (Alternative Minimum Tax) if you don't sell the stocks within the same tax year.
You have to report the "paper capital gains" for AMT purposes but that doesn't necessarily subject you to paying the AMT. And if it does, you will at least get AMT credits you can apply towards future tax years.