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

[Oldiesfreak1854]

President of the USA - George H. W. Bush (I was born two days before he left office)
Vice President of the USA - Dan Quayle (See above)
Monarch of the UK and other realms of the Commonwealth - Elizabeth II
Prime Minister of the UK - John Major
President or Premier of Russia or the Soviet Union - Boris Yeltsin
President of France - Francois Miterrand
Pope of the Catholic Church - John Paul II

Somewhat more difficult:

Speaker of the US House of Representatives - IDK
Majority Leader of the US Senate - IDK
Prime Minister of Canada - IDK
Prime Minister of Australia - IDK

Considerably trickier:

Governor of Massachusetts - Bill Weld
Governor of Illinois - Jim Edgar
UK Chancellor of the Exchequer - IDK
UK Leader of the Opposition - IDK
Most recent Best Picture Oscar winner - IDK
Most recent Nobel Peace Prize laureate - IDK

Very tough:

Senior U.S. Senator of Tennessee - IDK
Junior U.S. Senator of Vermont - Jim Jeffords
Leader of the Scottish National Party - IDK
Most recent Best Supporting Actor Oscar winner - IDK
Most recent Nobel laureate in Physics - IDK