What are Examples of Republic government?

Well, there's the People's Republic of China, the People's Republic of Ireland - others include Congo, USA, Germany, South Africa and Korea are just some examples, out of a lot. You can research more if you type "Democratic Republics" into google. Wikipedia has some info on exactly what a Democratic Republic is, so you might want to try looking there to help you narrow down your search, and they give a few examples. I hope this has helped answer your question. :)