This is not a complete list but does include the major awards.
IMDB lists most of his TV and film awards but does not have a complete list. Other online awards databases are Goldderby's The Lost Mind awards site and official sites for the awards organizations. There is also awards history mentioned in many of Christopher Plummer's bios released in connection with past films and stage work.

The Shakespeare Guild's 2006 Gielgud Award (NAC)

2002 National Board of Review, Career Achievement Award (NBR's site)

2001 Canada's Governor General Performing Arts Award (Ottawa Citizen)

1999 Los Angeles Film Critics Association Award for The Insider (Leonard Maltin's site)

1997 Tony Award for Barrymore (Getty images )

1974 Tony Award for Cyrano (Getty Images)

1962 Evening Standard Award for Becket (Corbis)

Juilliard honorary doctorate 1993(photo: Peter Schaff)

Shakespeare Theater at the Folger, Will Award (Washington Times April 24, 1990)

NYPL Literary Lions (1988)

Companion of the Order of Canada (Harry Palmer Gallery)

Companion of the Order of Canada (Ottawa Journal, September 26, 1970)

Great Britain's Evening Standard Award for Best Actor for Becket
Great Britain's Evening Standard Nomination for Best Actor for Danton's Death
Tony Award for Best Actor in a Play for Barrymore
Tony Award for Best Actor in a Musical for Cyrano
Tony Nomination for Best Actor in a Play for Inherit the Wind
Tony Nomination for Best Actor in a Play for King Lear
Tony Nomination for Best Actor in a Play for No Man's Land
Tony Nomination for Best Actor in a Play for Othello
Tony Nomination for Best Actor in a Play for J.B.
New York Drama Desk Award for Barrymore
New York Drama Desk Award for Othello
New York Drama Desk Award for Cyrano
New York Drama Desk Nomination for Inherit the Wind
New York Drama Desk Nomination for King Lear
New York Drama Desk Nomination for No Man's Land
Drama League Distinguished Performance Award for Cyrano
Drama League Honored Previous Recipient for King Lear
Outer Critics Circle Award for Barrymore
Outer Critics Circle Award for Cyrano
Outer Critics Circle Nomination for Inherit the Wind
Outer Critics Circle Nomination for No Man's Land
Theater World Award for The Dark Is Light Enough
Ovation Award (Los Angeles theater award) for Barrymore
Emmy Award for The Moneychangers (Outstanding Lead Actor in a Limited Series)
Emmy Award for Madeline (Outstanding Voice-Over Performance)
Emmy Nomination for the Our Fathers (Outstanding Supporting Actor in a Miniseries or a Movie)
Emmy Nomination for the Thornbirds (Outstanding Supporting Actor in a Limited Series or a Special)
Emmy Nomination for Hamlet at Elsinore (Outstanding Performance by an Actor in a Leading Role in a Drama)
Emmy Nominaton for Little Moon of Alban (Best Actor)
Golden Globe Nomination for American Tragedy - Best Supporting Actor
    in a Series, Mini-Series or Motion Picture Made for TV (2000)
Screen Actors Guild nomination for Our Fathers -
    Outstanding Performance by a Male Actor in a Television Movie or Miniseries (2006)
Screen Actors Guild Nomination - cast of A Beautiful Mind (2001)
Genie Award for Murder By Decree
Genie Nomination for The Amateur
Genie Nomination for Impolite
Genie Nomination for Ararat
Genie Nomination for Blizzard
Gemini Nomination for Counterstrike
Gemini Nomination for Harrison Bergeron
Los Angeles Film Critics Association Award for The Insider (1999)
National Society of Film Critics Award for The Insider (1999)
Golden Satellite Nomination for The Insider (1999)
Annie Award Nomination for voiceover for Babes in Toyland (1998)
Video Premiere Award Nomination for Full Disclosure (2001)
Austria's Golden Badge of Honor
Salzburg’s Chalice of Honour
Companion of the Order of Canada, 1968
Canadian Maple Leaf Award for Arts and Letters 1982
Canada's Commemorative Medal 1992
Canada's Walk of Fame 1999
Canada's Governor General Performing Arts Award 2001
Canadian Club of New York's Arts and Letters Award
Connecticut Lifetime Achievement Award 1994
Westport Arts Advisory Committee lifetime achievement award
Shakespeare Theater at the Folger - Will Award 1990
Inducted in NYC's Theatre Hall of Fame 1986
Boston critics Elliot Norton Award
City of Chicago Joseph Jefferson Award
New York Player's Club - Edwin Booth Award
National Arts Club - Gold Medal for Life Achievement in the Arts
Roundabout Theater's inaugural Jason Robards Award for Excellence in Theater 2002
National Board of Review of Motion Pictures - Career Achievement Award 2002
Honorary Doctorate of Fine Arts at New York's Juilliard School of Performing Arts 1993
Honorary Doctorate from Ryerson University, Toronto 2002
Honorary Doctorate from University of Toronto 2003
Honorary Doctorate from University of Western Ontario 2004
Gascon-Thomas Award from the National Theatre School of Canada 2004
Shakespeare Society Medal 2004
Honorary Doctorate from McGill University 2006
The Sir John Gielgud Award for Excellence in the Dramatic Arts aka The Golden Quill 2006

Christopher Plummer attended the November 1988 New York Public Library Literary Lions dinner as a special guest, and gave a reading at the close of the event. NYPL President Vartan Gregorian, introduced him as "a lion of the performing arts".