If you go beyond Europe and Aus/Can/US/NZ, William has visited officially: Bhutan, Botswana, China, India, Israel, Japan, Lesotho, Kenyax2, Kuwait, Malaysia, Namibia, Oman, Pakistan, Palestine, Singapore, Solomon Islands, South Africa, Tanzania, Tuvalu, Vietnam
Harry: Angola, Bahamas, Belize, Botswana, Brazil x2, Chile, a Carribean tour, Fiji, Jamaica, Japan, Lesotho x3, Malawi, Nepal, Oman, South Africa x2, UAEx2, Zambia, Tonga
Sorry, I added up wrong! Harry has done more (though a couple of the trips were for polo or rugby)