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

[DC Al Fine]

Easy(er):

President of the USA - Bill Clinton
Vice President of the USA - Al Gore
Monarch of the UK and other realms of the Commonwealth - Elizabeth
Prime Minister of the UK - John Major
President or Premier of Russia or the Soviet Union - Boris Yeltsin
President of France - Mitterand?
Pope of the Catholic Church - John Paul II

Somewhat more difficult:

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

Considerably trickier:

Governor of Massachusetts - William Weld
Governor of Illinois -
UK Chancellor of the Exchequer -
UK Leader of the Opposition - Neil Kinnock
Most recent Best Picture Oscar winner - Schindler's List
Most recent Nobel Peace Prize laureate -

Very tough:

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