Unlike us poor saps, the Windsors get to decide how much tax they pay, and whether they actually want to pay any tax at all.
For example the Queen wasn't required to pay inheritance tax on the Queen Mother's estate, and the will was made private (wills are normally public documents) so no one outside the Royal family knows how much tax was avoided.
The Queen volunteers to pay some income tax (after a generous deduction of expenses naturally - roast swan isn't cheap).
Charles' income derives from the Duchy of Cornwall. It (like the Duchy of Lancaster that creates income for the Queen) is exempt from both corporate and capital gains tax. No one is quite sure why.
Charles voluntarily agrees to pay some tax on this income (to stop the peasants revolting one assumes). However, since the accounts are closed (unlike every normal business in the UK that has to submit accounts to the taxman) its not clear exactly how much tax is being avoided by these exemptions.
Next time you get your payslip and see the large chunk the government has taken out of it, or have to pay a large inheritance tax bill on a deceased relative's estate, at least you can console yourself with the thought that part of these taxes are being used to support the Windsors living in their numerous homes. And that the Windsors are exempt from the taxes you have to pay.
The Telegraph - Watchdog investigates Charles' tax record
The Guardian - MPs angry at confidential royal will and tax deal