morarji desai
Morarji Desai was the first Indian prime minister to resign from office. He resigned in July of 1979 after serving just slightly over two years of the five year term.
Either the cabinet minister has to resign (if the cabinet still supports the Prime Minister), or if the cabinet no longer supports the Prime Minister the Prime Minister has to resign (resulting in a party election) or the Prime Minister can call a general election.
In the UK the Prime Minister can "reshuffle" his cabinet and take the minister out, stripping them of their position; but they are still an MP.
October 2007, at the end of Prime Minister Shaukat Aziz'stenure...
The Queen appoints the Prime Minister and as such, can make him or her resign. However, typically the two communicate regularly on governmental matters and maintain a balance of power.
Sir Mackenzie Bowell was the only Prime Minister of Canada to be forced to resign. http://canadaonline.about.com/cs/primeminister/p/pmbowell.htm
Austria. Prime Minister Schuschnigg was forced to resign after attempting to hold a referendum in order to stop the spreading German influence. The next Prime Minister of Austria was a Nazi, and allowed the annexation of Austria into Nazi Germany.
Mackenzie Bowell
Margaret Thatcher, who is indeed the ONLY female Prime Minister Britain has ever had. She was elected on 4th May 1979, and was in office until 28th November 1990, when domestic unpopularity forced her to resign.
Stephen Harper became the Prime Minister once in 2006. He has continued to be re-elected in 2008, with an election pending in 2011. So far he has not had to resign as Prime Minister.
Gough Whitlam
At the beginning of World War one the Prime Minister of Italy was Vittorio Orlando but after the war ended he was forced to resign.