When you were born, and without Googling or Wiki-ing....

[Wake Me Up When The Hard Border Ends]

April 1991

Easy(er):

President of the USA - George H.W. Bush
Vice President of the USA - Dan Quayle
Monarch of the UK and other realms of the Commonwealth - Queen Elizabeth II
Prime Minister of the UK - John Major
President or Premier of Russia or the Soviet Union - Mikhail Gorbachev
President of France - Francois Mitterand
Pope of the Catholic Church - John Paul II

Somewhat more difficult:

Speaker of the US House of Representatives - No idea
Majority Leader of the US Senate - No idea
Prime Minister of Canada - Brian Mulroney
Prime Minister of Australia - Bob Hawke

Considerably trickier:

Governor of Massachusetts - No idea
Governor of Illinois - No idea
UK Chancellor of the Exchequer - Norman Lamont
UK Leader of the Opposition - Neil Kinnock
Most recent Best Picture Oscar winner - No idea
Most recent Nobel Peace Prize laureate - No idea

Very tough:

Senior U.S. Senator of Tennessee - No idea
Junior U.S. Senator of Vermont - No idea
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