A patent office is a governmental or intergovernmental organization which controls the issue of patents. In other words, "patent offices are government bodies that may grant a patent or reject the patent application based on whether the application fulfils the requirements for patentability."
For a list of patent offices and their websites, see the World Intellectual Property Organization (WIPO) maintained list, here.
The entries shown in italics are regional or international patent offices.
African Regional Intellectual Property Organization (ARIPO)
IP Australia (IPA)
Barbados Corporate Affairs and Intellectual Property Office (CAIPO)
Canadian Intellectual Property Office (CIPO)
Ethiopian Intellectual Property Office (EIPO)
European Patent Office (EPO)
Eurasian Patent Organization (EAPO)
German Patent Office (DPMA)
Gulf Cooperation Council (GCC) Patent Office (GCCPO)
Indian Patent Office (IPO)
Intellectual Property Office of Singapore (IPOS)
Israeli Patent Office
Italian Patent and Trademark Office
Japan Patent Office (JPO)
Korean Intellectual Property Office (KIPO)
Mexican Institute of Industrial Property (IMPI)
National Industrial Property Institute, France (INPI)
National Industrial Property Institute, Portugal (INPI)
Netherlands Patent Office
Nordic Patent Institute (NPI)
Norwegian Industrial Property Office
"Organisation Africaine de la Propriété Intellectuelle" (OAPI)
Patent Office of the Republic of Latvia
Polish Patent Office (PPO)
Russian Federal Service for Intellectual Property, (Rospatent), Russian Federation
Spanish Patent and Trademark Office (SPTO)
State Intellectual Property Office of the People's Republic of China (SIPO)
Swedish Patent and Registration Office (PRV)
Swiss Federal Institute of Intellectual Property (IGE)
Taiwan Intellectual Property Office, (TIPO), Republic of China
Turkish Patent Institute
Ukrainian Patent Office (officially 'State Enterprise "Ukrainian Institute of Industrial Property"', or 'SE "UIPV"')
United Kingdom Intellectual Property Office, (UK-IPO)
United States Patent and Trademark Office (USPTO)
World Intellectual Property Organization (WIPO)
Confederate States Patent Office
"Goskomizobretenie" (Soviet Union patent office)
International Patent Institute