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

[Joe Biden 2020]

April 29, 1982

President of the United States - Ronald Wilson Reagan
Vice President of the United States - George Herbert Walker Bush
Queen Elizabeth II
Prime Minister of the UK: Margaret Thatcher
Pope: John Paul II

Speaker of the House - Tip O'Neill (maybe Carl Albert, can't remember)
Senate Majority Leader - Bob Dole, I presume.

Governor of Massachusetts - Michael Dukakis

Senior US Senator of Tennessee - Al Gore

Extra Credit:

Governor of Oklahoma - George Nigh (D)
Governor of Arkansas - William Jefferson Clinton (D)

WHOOPS:  I got one wrong - Speaker was Tip O'Neill, but Maj Leader was not Bob Dole, it was Howard Baker.

[Joe Biden 2020]

April 1995:

President of the USA - Bill Clinton
Vice President of the USA - Al Gore
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 - Jacques Chirac?
Pope of the Catholic Church - Pope Benedict XIV

Speaker of the US House of Representatives - Newt Gingrich
Majority Leader of the US Senate - Tom DeLay?
Prime Minister of Canada - Jean Charest
Prime Minister of Australia - Paul Keating?

Considerably trickier:

Governor of Massachusetts - William Weld??
Governor of Illinois -
UK Chancellor of the Exchequer -
UK Leader of the Opposition - Tony Blair?
Most recent Best Picture Oscar winner -
Most recent Nobel Peace Prize laureate - Nelson Mandela/W.F De Klerk??

Very tough:

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

Try that one again.