President of the USA - Billy Jeff
Vice President of the USA - The Inventor of the Internet.
Monarch of the UK and other realms of the Commonwealth - Guess... (hint: I am not over 61)
Prime Minister of the UK - Major
President or Premier of Russia or the Soviet Union - The Drunkard
President of France - Mitterrand (good thing you didn't ask who was the PM... I'm not idea when in the year Balladur succeeded Bérégovoy...)
Pope of the Catholic Church - JP2
Speaker of the US House of Representatives - No idea, I don't know the dates of any speaker before Gingrich... Was Tip O'Neill still around, by chance?
Majority Leader of the US Senate - No Freaking Idea
Prime Minister of Canada - Campbell or Chrétien... Gonna say Campbell.
Prime Minister of Australia - Keating, pretty sure about this one
Governor of Massachusetts - Pretty sure it was Weld
Governor of Illinois - No idea, I don't know any.
UK Chancellor of the Exchequer - No idea
UK Leader of the Opposition - Hum... John Smith?
Most recent Best Picture Oscar winner - No idea
Most recent Nobel Peace Prize laureate - No idea
Senior U.S. Senator of Tennessee - Howard Baker?
Junior U.S. Senator of Vermont - Jim Jeffords?
Leader of the Scottish National Party - No idea
Most recent Best Supporting Actor Oscar winner - No idea
Most recent Nobel laureate in Physics - No idea