It seems that the page I provided below in my old answer only shows one type of the taxes and not the full airport taxes (as mentioned in a comment by Doc). So my answer at best is partially correct.
Anyway, the only resource I found for the full taxes is again from IATA's website (IATA List of Ticket and Airport Taxes and Fees), which is a paid PDF file/CD Rom and it costs ($2,671.00), this is too much for such a resource, and most likely the sum of taxes you will pay for the coming 10 years will be less than this amount. Anyway, searching Google did return this PDF file from another websites, I do not know if downloading it will be legal or not, but it is there!
Another option is: in Kayak.com, after selecting a fare, it will show the sum of taxes to be paid, this sum will include the airport taxes, along with other taxes so it is the closest figure you can get, for free.
As usual, IATA's website provide such information. The Customs, Currency & Airport Tax regulations page provides a lot of information including airport taxes in the selected country (you have to click "more about tax" to see full airport tax information). Here is an example of airport tax in Indonesia: