Although it has been proved to be "inaccurate" in some respects, I found this on Wikipedia:-
http://en.wikipedia.org/wiki/Father's_Day
Third Sunday of June
Argentina, Bahamas, Bangladesh, Bulgaria, Canada, Chile, China, Colombia, Costa Rica, Cuba, Cyprus, France, Greece, Guyana, Hong Kong, India, Ireland, Jamaica, Japan, Malaysia, Malta, Mauritius, Mexico, Netherlands, Pakistan, Panama, Paraguay, Peru, Philippines, Puerto Rico, Singapore, Slovakia, South Africa, Sri Lanka, Switzerland, Trinidad and Tobago, Turkey, United Kingdom, United States, Venezuela, Zimbabwe
June 23
Nicaragua, Poland, Uganda
July 30
Vietnam
Second Sunday of July
Uruguay
Last Sunday of July
Dominican Republic
Second Sunday of August
Brazil
August 8
Taiwan
First Sunday of September
Australia, New Zealand
New Moon of September (Bhadra as per Lunar Calendar) (don't understand this one)
September 11
Nepal
Second Sunday of November
Estonia, Finland, Norway, Sweden
December 5
Thailand
February 23
Russia, Ukraine, Belarus
14 March (24 Esfand)
Iran
March 19
Bolivia, Honduras, Italy, Liechtenstein, Portugal, Spain
May 5
Romania
May 8
South Korea (Parents' Day)
Ascension Day
Germany
First Sunday of June
Lithuania
June 5 (Constitution Day)
Denmark
Second Sunday of June
Austria, Belgium, Ecuador
June 17
El Salvador, Guatemala
It will probably be better looking at the web page, but the list gives a general idea.