Mifune's image as a chambara god gives him an iconic status I believe at least on par with Nicholson or Newman. The name might not be well-known in the West, but whenever anybody thinks samurai they most likely think of him. In acclaim he is probably far below them (in awards anyway), though he does have a Hollywood star, which is impressive.

Compromise time:

1. Laurence Olivier
2. Paul Newman
3. Toshiro Mifune
4. Jack Nicholson
5. Al Pacino
6. Marcello Mastroianni
7. Gregory Peck
8. Peter O'Toole
9. Robert Mitchum
10. Michel Piccoli
11. Sean Penn
12. Tatsuya Nakadai
13. Philippe Noiret
14. Bill Murray
15. Gary Oldman
16. Walter Matthau
17. Yves Montand
18. Steve McQueen
19. Ian McKellen
20. Paul Muni
21. Liam Neeson
22. David Niven
23. Edward Norton
24. Thomas Mitchell
25. Nanni Moretti
26. Joel McCrea
27. Viggo Mortensen
28. Joe Pesci
29. Joaquin Phoenix
30. Victor McLaglen
31. Armin Mueller-Stahl
32. Matthew McConaughey
33. Franco Nero
34. Robert Montgomery
35. Nick Nolte
36. Ulrich Mühe
37. Masahiro Motoki

Another late thought: Why is Cage so low in his group? It's just dazzling to see him below names like Bing Crosby and Willem Dafoe, and with Damon and him that far apart. Not only do I think that he should be higher than these names, but I'd even say that it is not a close call.

He is a top 50 in popularity alone, and memes and Community jokes aside, he is also well acclaimed among "serious" critics as well. You don't get to be one of the few modern actors in TSPDT's Shooting Gallery for no reason.
As for his filmography, well...Adaptation, Con Air, Leaving Las Vegas, Raizing Arizona, Peggy Sue Got Married, Birdy, Red Rock West, Face/Off, Bad Lieutenant, Matchstick Man, Honeymoon in Vegas ...that's definitely a strong, acclaimed and diverse filmography. I'd say it is more solid than Damon's, and definitely more solid than Crosby's or Dafoe's. Plus, most of these are films with him as a lead and where his performance was a key part of the overall success, so it's not just a question of him just "being there". Even now, he still puts on one or two remarkable performances, such as in Joe or The Croods, to remind us that he CAN still act.

I'm not a fan of his, but it just seems unfair of us to penalize Cage so much for his bad choices and then forgive legends such as Brando for decades and decades of bad movies. He is popular, bankable, acclaimed and all in all one of the greatest actors of the last 30 years.
As Ethan Hawke once said, "If I could erase his bottom half bad movies, and only keep his top half movies, he would blow everyone else out of the water."

I can see that part of list being re-arrenged:

21. Bing Crosby
22. Nikolay Cherkasov
23. Joseph Cotten
24. Willem Dafoe
25. Tom Courtenay
26. Choi Min-Sink
27. Nicolas Cage

maybe into something like this:

21. Nikolay Cherkasov
22. Choi Min-Sink
23. Nicolas Cage
24. Joseph Cotten
25. Willem Dafoe
26. Tom Courtney
27. Bing Crosby

Mifune does have three Blue Ribbon awards and Honorary Japanese Academy award which isn't too shabby. Plus I'd say this is the case when gap in acclaim is much smaller than awards' tally indicates.

Wah huh? Con Air is not exactly a great movie--it's legacy rests on falling into "so bad it's good" territory"--and Cage's performance is regularly criticized. If you're trying to make a case for Cage as a great actor, Con Air is usually one of the obstacles to the argument. That aside, making the case that his filmography is stronger than Damon's is ridiculous. Not only does he have the massive Borne trilogy and a part in the Ocean's movies, he also has various acclaimed performances in big movies like Good Will Hunting, The Departed, True Grit, The Informer, Invictus, Dogma, Mr. Ripley, Saving Private Ryan, The Martian, Behind the Candelabra, Syriana, Inside Job, Contagion and others. He's a very major box office star, and has had very few duds, and cancels each one out with plenty of quality work. Cage's biggest heel is his filmography.

1. Sidney Poitier
2. Peter Sellers
3. George C. Scott
4. Anthony Quinn
5. Robert Redford
6. Edward G. Robinson
7. Takashi Shimura
8. Michel Simon
9. Chishu Ryu
10. Mickey Rooney
11. Vincent Price
12. Mack Sennett
13. Geoffrey Rush
14. Omar Sharif
15. Brad Pitt
16. Ralph Richardson
17. Fernando Rey
18. Maximilian Schell
19. Michel Serrault
20. Claude Rains
21. Paul Robeson
22. Jason Robards
23. William Powell
24. George Sanders
25. Paul Scofield
26. Robert Shaw
27. Martin Sheen
28. Alan Rickman
29. Michael Redgrave
30. Walter Pidgeon
31. Tim Robbins
32. Robert Ryan
33. Jürgen Prochnow
34. Roy Scheider
35. Mickey Rourke
36. Mark Ruffalo
37. Oliver Reed

About the Cage-order, I think I prefer something like this.

21. Nikolay Cherkasov
22. Choi Min-Sik
23. Joseph Cotten
24. Willem Dafoe
25. Nicolas Cage
26. Tom Courtney
27. Bing Crosby

I think Cotten and Dafoe have a stronger body of work, and have fewer flaws in their filmography. Dafoe is also at least as acclaimed as Cage, and Cotten is one of the actors who got snubbed by the Academy on numerous occasions (Citizen Kane, Shadow of a Doubt, The Third Man).

My take for this group:

1. Sidney Poitier
2. Peter Sellers
3. George C. Scott
4. Anthony Quinn
5. Robert Redford
6. Edward G. Robinson
7. Takashi Shimura
8. Michel Simon
9. Chishu Ryu
10. Mickey Rooney
11. Vincent Price
12. Mack Sennett
13. Geoffrey Rush
14. Brad Pitt
15. Omar Sharif
16. Ralph Richardson
17. Fernando Rey
18. Claude Rains
19. Maximilian Schell
20. Michel Serrault
21. Paul Robeson
22. George Sanders
23. Paul Scofield
24. Robert Shaw
25. Jason Robards
26. Martin Sheen
27. Robert Ryan
28. William Powell
29. Alan Rickman
30. Alastair Sim
31. Michael Redgrave
32. Walter Pidgeon
33. Tim Robbins
34. Roy Scheider
35. Jürgen Prochnow
36. Mickey Rourke
37. Mark Ruffalo
38. Oliver Reed

Erm, isn't Alastair Sim missing in your list, Tim? :P
We are very close, I only think that especially Robert Ryan has to move up a few spots in your list. He has an exceptional body of work, and was one of the essential supporting actors in the 1940s, 1950s and 1960s - often a tough character. Some of his films are true classics, and he delivers essential performances in them: Crossfire, The Set-Up, The Naked Spur, Bad Day at Black Rock, The Professionals, The Dirty Dozen, The Wild Bunch and The Iceman Cometh, for example.

1. Sidney Poitier
2. Peter Sellers
3. George C. Scott
4. Anthony Quinn
5. Robert Redford
6. Edward G. Robinson
7. Takashi Shimura
8. Michel Simon
9. Chishu Ryu
10. Mickey Rooney
11. Vincent Price
12. Brad Pitt
13. Mack Sennett
14. Geoffrey Rush
15. Omar Sharif
16. Ralph Richardson
17. Fernando Rey
18. Claude Rains
19. Maximilian Schell
20. Michel Serrault
21. Paul Robeson
22. George Sanders
23. Paul Scofield
24. Robert Shaw
25. Jason Robards
26. Martin Sheen
27. Robert Ryan
28. Alan Rickman
29. William Powell
30. Alastair Sim
31. Michael Redgrave
32. Walter Pidgeon
33. Tim Robbins
34. Roy Scheider
35. Jürgen Prochnow
36. Mickey Rourke
37. Mark Ruffalo
38. Oliver Reed

It is definitely strong and diverse, but terribly uneven. He worked with auteurs, indie directors, in blockbusters, dramas, comedy, action, sci-fi...and he was always a key part of the film. If the script is good, he can do magic, and even the flops are entertaining thanks to his performances...which reminds me of the Dustin Hoffman quote that "even the worst Brando films are interesting because of him..." - please note that I'm not comparing Cage to Brando :) -
He is one of the very few actors that will always put on a memorable performance regardless of the quality of the film, and that is exactly why he is still popular despite all the flops, in a world where most careers die after a flop or two.

As for his acclaim, this beautiful Ebert quote alone is a wonderful testament to his acclaim, talent and versatility:
"...And Cage. There are often lists of the great living male movie stars: De Niro, Nicholson and Pacino, usually. How often do you see the name of Nicolas Cage? He should always be up there. He's daring and fearless in his choice of roles, and unafraid to crawl out on a limb, saw it off and remain suspended in air. No one else can project inner trembling so effectively. Recall the opening scenes in "Leaving Las Vegas." See him in Scorsese's "Bringing Out the Dead." Think of the title character in "The Weather Man." Watch him melting down in "Adaptation." And then remember that he can also do a parachuting Elvis impersonator ("Honeymoon in Vegas"), a wild rock 'n' roller ("Wild at Heart"), a lovesick one-handed baker ("Moonstruck"), a straight-arrow Secret Service agent ("Guarding Tess") and on and on."

I think it is safe to say that he is more acclaimed than Damon, Crosby or Dafoe, and at least as popular.

I agree. That would be an improvement, Tim. Although some names in the 15-20 section should be part of the discussion as well.

1. Sidney Poitier
2. Anthony Quinn
3. Peter Sellers
4. George C. Scott
5. Takashi Shimura
6. Michel Simon
7. Robert Redford
8. Chishu Ryu
9. Edward G. Robinson
10. Mickey Rooney
11. Mack Sennett
12. Geoffrey Rush
13. Omar Sharif
14. Vincent Price
15. Maximilian Schell
16. Brad Pitt
17. Ralph Richardson
18. Fernando Rey
19. Michel Serrault
20. Claude Rains
21. George Sanders
22. Paul Scofield
23. Paul Robeson
24. Jason Robards
25. Robert Shaw
26. Martin Sheen
27. Robert Ryan
28. William Powell
29. Alan Rickman
30. Alastair Sim
31. Roy Scheider
32. Michael Redgrave
33. Walter Pidgeon
35. Tim Robbins
36. Oliver Reed
37. Mickey Rourke
38. Mark Ruffalo

I think Dafoe for one belongs over Cage. Really strong filmography, at least matching but more likely surpassing Cage's: Platoon, Last Temptation of Christ, Wild at Heart, The English Patient, Shadow of the Vampire, Spider-Man, Finding Nemo, The Life Aquatic with Steve Zissou, Nymphomaniac, The Grand Budapest Hotel, The Fault in Our Stars and there are more. Unlike Cage he's primarily supporting actor, but one of most high profile ones.

Current group will probably ends up something like this:

1. Sidney Poitier
2. Peter Sellers
3. Anthony Quinn
4. George C. Scott
5. Robert Redford
6. Edward G. Robinson
7. Takashi Shimura
8. Michel Simon
9. Chishu Ryu
10. Mickey Rooney
11. Vincent Price
12. Mack Sennett
13. Geoffrey Rush
14. Omar Sharif
15. Brad Pitt
16. Ralph Richardson
17. Fernando Rey
18. Maximilian Schell
19. Claude Rains
20. Michel Serrault
21. Paul Robeson
22. George Sanders
23. Paul Scofield
24. Robert Shaw
25. Jason Robards
26. Martin Sheen
27. Robert Ryan
28. William Powell
29. Alan Rickman
30. Alastair Sim
31. Michael Redgrave
32. Walter Pidgeon
33. Tim Robbins
34. Roy Scheider
35. Jürgen Prochnow
36. Mickey Rourke
37. Mark Ruffalo
38. Oliver Reed

I for one think Quinn probably belongs over Scott. More influential and prolific (although quite uneven filmography) and very acclaimed at his peak.

1. James Stewart
2. John Wayne
3. Spencer Tracy
4. Denzel Washington
5. Max von Sydow
6. Orson Welles
7. Rudolph Valentino
8. Totò
9. Robin Williams
10. Jean-Louis Trintignant
11. Conrad Veidt
12. Christopher Walken
13. Rod Steiger
14. Alberto Sordi
15. Jon Voight
16. Donald Sutherland
17. Kevin Spacey
18. Jacques Tati
19. Erich von Stroheim
20. Innokenty Smoktunovsky
21. Will Smith
22. Gene Wilder
23. Ugo Tognazzi
24. Stellan Skarsgård
25. Gian Maria Volonte
26. Eli Wallach
27. Benicio Del Toro
28. Harry Dean Stanton
29. Paul Winfield
30. John Travolta
31. James Woods
32. Richard Widmark
33. Frank Sinatra
34. Forest Whitaker
35. Billy Bob Thornton
36. Anatoliy Solonitsyn
37. Raf Vallone