I don't feel I've seen enough to make a list of the greatest ones, so I'll give some sort of an honored list, or maybe a few that just haven't been mentioned yet.
Mickey Rourke - The Pope of Greenwich Village (Hearing good things about The Wrestler, too)
Viggo Mortensen & David Morse - The Indian Runner (Penn's greatest film)
Ed Harris - A History of Violence (Hurt was great, but Harris was even better)
James Coburn - Cross of Iron / Affliction (Didn't see his name yet, intense guy)
Warren Beatty - Bugsy/Bulworth (Two whacky, wild performances from this heart-throb)
John Goodman - The Big Lebowski (Shut the F up, Donnie! Best comedic performance maybe of all-time)
Jack Nicholson - Reds (The ultimate Nicholson can be found in much more energetic performances, but the subdued portrayal of O'Neal is one of his most interesting)
Kris Kristofferson - Heaven's Gate (No comment)
Robert Redford - All the President's Men (I believe this is Redford's best work)
Charles Grodin - Midnight Run (Co-starring Robert De Niro, highly recommended)
There were a couple of actors where I couldn't decide between a performance so I gave both a nod.

my top 10:
Marlon Brando - Last Tango in Paris
Jack Nicholson - One Flew Over The Cuckoo's nest or The Shining
Robert De Niro - Taxi Driver
Al Pacino - Dog Day Afternoon
Dustin Hoffman - Straw Dogs
Steeve McQueen - Papillon
Paul Newman - Cool Hand Luke
Kirk Douglas - Paths of Glory
Emily Watson - Breaking The Waves
Peter Sellers - Dr. Strangelove
Honorable mention:
Michael Caine - Sleuth
Vincent D'Onofrio - Full Metal Jacket
Max Von Sydow - Hour of The Wolf or Three Days of Condor
Daniel Day Lewis - There Will Be Blood
Isbella Huppert - The Piano Teacher
Henry Fonda - Once Upon A Time in the West
Cline Eastwood - The Good, The Bad and The Ugly or Dirty Harry
Gene Hackman - The Conversation or The French Connection
John Malkovich - Being john Malkovich
Toshiro Mifune - Throne of Blood
Takashi Shimura - Ikiru
Peter FInch - Network
Ellen Burstyn - Requiem For A Dream
Matthew Broderick - Ferris Bueller's Day Off or The Election
Amrish Puri - Ghatak

David Carradine - Kill Bill
Henry Fonda - 12 Angry Men
Gene Hackman - The Conversation
Marlon Brando - Apocalypse Now
Gregory Peck - To Kill A Mockingbird
Clint Eastwood - The Good, The Bad & The Ugly
Marcello Mastroianni - 8 1/2
Roberto Benigni - La Vita E Bella
Morgan Freeman - Shawshank Redemption
Kevin Spacey - American Beauty

Haven't seen enough movies (particularly oldies) to pick a top ten, but here are some good leads from oldies (pre-1970) and more recent films in no particular order.
Leading Actor - Oldies
1-Marlon Brando (Streetcar Named Desire)
2-Frederick March (Inherit the Wind)
3-Spencer Tracy (Inherit the Wind)
4-Paul Newman (The Hustler or Cool Hand Luke)
5-Rod Steiger (Heat of the Night, The Pawnbroker)
6-Peter Sellers (Dr. Strangeglove)
7-Humphrey Bogart (Treasure of Sierra Madre)
8-Ray Milland (Lost Weekend)
9-Burt Lancaster (Elmer Gantry)
10-Frank Sinatra (Man with a Golden Arm)
Leading Actor - since 1970
1-George C. Scott (Patton)
2-Dustin Hoffman (Rainman)
3-Robert Duvall (The Apostle)
4-Jack Nicholson (One Flew Over Cuckoo's Nest, Chinatown)
5-Jack Lemmon (Glengarry Glen Ross, Save the Tiger)
6-Jamie Foxx (Ray)
7-Robert DeNiro (Raging Bull)
8-Al Pacino (Godfather II)
9-Phillip Seymour Hoffman (Capote)
10-Roberto Begnini (Life is Beautiful)
Also, some great Supporting Actors: Robert DeNiro (Godfather II), George C. Scott (The Hustler), John Houseman (Paper Chase), Martin Landau (Tucker), John Casale (Godfather II), Alec Baldwin (Glengarry Glen Ross), Joe Peschi (Goodfellas), Walter Huston (Treasure of Sierra Madre), George Kennedy (Cool Hand Luke), Al Pacino (Dick Tracy)
Of course, the subject is highly debatable.

Pyro - great call on Robert Duvall. That is a great mini-series based on a fantasic book. Many great performances but Duvall's is the most exceptional.
Many great actors listed in these posts. Sometimes hard to pick their best performance.
I'll nominate:
Liam Neeson for Rob Roy (liked Schindlers List better, but his performance in RRoy seemed more memorable).
Another poster had William Hurt for A History of Violence. I think he has had better performances in Body Heat, Broadcast News or Children of a Lesser God.
Russell Crowe for A Beautiful Mind. He won an Oscar, I think, for Gladiator. But I thought his performances were better in Beautiful Mind and The Insider.

No mention of Marlon Brando in Last Tango in Paris from anyone? I hated the movie but he was undeniably incredible in that movie, much better than in the Godfather.

For the 10 Best in no particular order:

1. Paul Newman (The Hustler)
2. Al Pacino (The Godfather Part II)
3. Clint Eastwood (The Good, the Bad and the Ugly)
4. Peter Finch (Network)
5. Martin Landau (Crimes and Misdemeanors)
6. Peter Sellers (Dr. Strangelove)
7. George C. Scott (Patton)
8. Edward Norton (American History X- 25th Hour- Fight Club)
9. Robert Duvall (Lonesome Dove)
10. Robert Deniro (Taxi Driver)
    "Walk down the right back-alley in Sin City, and you can find anything."

All these talk and no one mentions Montgomery Cliff in A Place in the Sun?

You forgot Mariah Carey in "Glitter" and Britney Spears in "Crossroads."

WellI'm really of the opinion that Worst Performances belongs in a completely separate thread, but I'll bite this time:
(once again, in no particular order)
John Wayne - The Conqueror (I agree 100%. One of the worst performances EVER in the history of filmdom, IMO.)
Jeff Goldblum - Earth Girls Are Easy
Nicolas Cage & Angelina Jolie - Gone In Sixty Seconds (I'm still not sure whose acting was the worst amongst the two, so both of them get a Razzberry for this turkey of a film. See the original Gone In Sixty Seconds instead, if possible. The 40+ min. car chase scene at the end of film is breathtaking.)
Wings Hauser - The Defense of Firebase Gloria
Casper Von Dien - Shark Attack
Kevin Costner - Robin Hood, Prince of Thieves (Makes me want to drive 12 inch needle spikes into my eyes & ears)
Keanu Reeves - Bram Stoker's Dracula (an emu with birth defects could out-act Reeves.)
Jean-Claude Van Damme - Double Impact (A double helping of crappiness!)
Burt Reynolds - Stroker Ace
John Travolta - Battlefield Earth
I'm really trying my best here to keep from speaking ill of the dead. There are lots of other performances from older actors that came to mind, but I'm just far too polite to list them here.
Honorable Mentions:
Matthew McConaughey - The Return of the Texas Chainsaw Massacre (three words: remote control leg)
Mario Van Peebles - Heartbreak Ridge
Everett McGill - The People Under The Stairs
Arnold Schwarzenegger - The Running Man (Did ANYONE making this film EVER bother to READ THE #@$%@#% SHORT STORY!?!)
Kate Beckinsale - Van Helsing
Bill Cosby - Leonard Part 6
Ice-T - Johnny Mnemonic
William H. Macy - Wild Hogs
Rutger Hauer - Buffy the Vampire Slayer
Tom Laughlin - The Trial of Billy Jack

Booty TimeBooty TimeAcross The U.S.AAAA!

Some great choices. On the opposite side the WORST ten/eleven performances.
Frank Sinatra-The Pride and the Passion/ Laughable accent
Montgomery Clift-Suddenly, Last Summer/ In a Coma
Liz Taylor-The Mirror Cracked/ Like an Egyptian Mummy on roller bearings
Kevin Costner-Robin Hood, Prince of Thieves/ A cigar store Indian would be more animated
Candace Bergen-Ghandi/ WTF?
Paul Newman-The Silver Chalice/ A beautiful but empty vessel
Suzy Parker- Kiss Them For Me/ This is acting?
Tom Cruise- Mission Impossible II/ It was impossible
Cary Grant- Howards of Virginia /Hyperkinetic
Barbra Streisand- Meet the Fockers/ Indescribably bad
John Wayne- The Conqueror/Unintentionally funny

In no particular order
Toshiro Milfune - Yojimbo
Joe Pesci - Goodfellas
Ron Pearlman - La Cit Des Enfants Perdus
Spencer Tracy - Bad Day at Black Rock
Al Pacino - Godfather part 2
Paul Newman - The Hustler
Steve McQueen - Papillon
R. Lee Ermey - Full Metal Jacket
Clint Eastwood - Il Buono, Il Brutto, Il Cattivo
George C. Scott - Patton
Honorable mentions:
Tatsuya Nakadai - Seppuku
Robert Redford - The Sting
James Stewart - Vertigo
James Earl Jones - Conan the Barbarian(!?!)
Jack Nicholson - One Flew Over the Cuckoo's Nest
Anthony Hopkins - Silence of the Lambs
Gary Cooper - High Noon
Christopher Lee - Dracula Has Risen from the Grave
Boris Karloff - Bride of Frankenstein
Peter O'Toole - The Lion in Winter

Booty TimeBooty TimeAcross The U.S.AAAA!

In no particular order:
Al Pacino - Dog Day Afternoon
Robert De Niro - Raging Bull
Marlon Brando - On the Waterfront/The Godfather
Tom Hanks - Forrest Gump
Gene Hackman - Unforgiven
Christopher Walken - The Deer Hunter
Paul Newman - The Hustler
Dustin Hoffman - Rain Man
Jack Nicholson - One Flew Over the Cuckoo's Nest
Denzel Washington - Glory

Richard Burton The Spy Who Came in from the Cold and Becket

1-Robert De Niro (Raging Bull-Taxi Driver)
2-Harvey Keitel(Bad Lieutenant)
3-Christian Bale(The Machinist)
4-Tom Hanks(Philadelphia)
5-Al Pacino(Scarface-Serpico-Cruising)
6-Leonardo DiCaprio (The Basketball Diaries)
7-Jack Nicholson(The Shining)
8-Joaquin Phoenix(Walk The Line)
9-Christopher Walken(The Deer Hunter)
10-Sean Penn(I Am Sam-The Assassination Of Richard Nixon)

Top Four Greatest Actor Performances:

1. George C. Scott in Patton
2. George C. Scott in The Hustler
3. George C. Scott in Dr. Strangelove
4. George C. Scott in Anatomy of a Murder
   Ok, some were supporting actor

1.Robert De Niro - Raging Bull
2.George C.Scott - Patton
3.Peter Sellers - Dr Strangelove
4.Takashi Shimura - Ikiru
5.Al Pacino - Dog Day Afternoon
6.Marlon Brando - On The Waterfront
7.Daniel Day Lewis - My Left Foot
8.William Holden - Sunset Blvd.
9.Jack Lemmon - The China Syndrome
10.Henry Fonda - On Golden Pond

1. Marlon Brando- "On the Waterfront"
2. Denzel Washington- "Malcolm X"
3. Al Pacino- "Dog Day Afternoon"
4. Sean Penn- "Dead Man Walking"
5. Robert De Niro- "Raging Bull"
6. Tom Hanks- "Forrest Gump"
7. Meryl Streep- "Sophie's Choice"
8. Robert Mitchum- "Night of the Hunter"
9. Humphrey Bogart- "Casablanca"
10. Jimmy Stewart- "Vertigo"
    Honorable mention for:
    Gene Hackman- "The Conversation"
    Jack Nicholson- "Chinatown"
    Val Kilmer- "Tombstone"
    Anthony Hopkins- "The Silence of the Lambs"
    Jack Lemmon- "Glengarry GlenRoss"
    Liv Ullman- "Persona"
    Jim Carrey- "The Truman Show"
    Ingrid Bergman- "Notorius"
    Toshiro Mifune- "Throne of Blood"
    Anthony Perkins- "Psycho"
    All, naturally, subject to change.
    But then the African swallow's non migratory

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1 Dustin Hoffman ( The Rain man)
2 Daniel Day-lewis ( My left foot)
3 Omar Sharif ( Dr Zivago)
4 Robert Donate( Goodbye Mr Chips)
5 Marlon Brando ( God Father)
6 Tom Hanks ( Philedelphia)
7 Robert De NIro( Raging Bull)
8 Peter O Tool ( Lawrance of Arabia)
9 Daniel Day Lewis( Gangs of Newyork)
10 Ben Kingsley ( Gandhi)

Tony Leung definitely deserves a spot! Thanks!

No Particular order

1. Paul Newman for .- The Verdict
2. Jean Louis Trigtinat .- Three Colors : Red
3. Al Pacino .- Dog Day Afternoon
4. William Hurt .- A History of Violence
5. Jack Lemmon .- Missing
6. Bruno Ganz .- Downfall
7. Daniel Day Lewis .- In the name of the father
8. Tony Leung Chiu Wai .-In the mood for love
9. Joel Grey .- Cabaret
10. Toshiro Mifune .- Yojimbo
11. Roy Scheider.- All That Jazz
12. Hugh Laurie .- House M.D. (for at least 3 episodes)

Here is my current top ten Actor performances. Chances are they will completely different tomorrow. I have also decidied to do a maximum of one film per actor.
In no particular order:

1. Robert De Niro- Taxi Driver
2. Peter O'Toole- Lawrence of Arabia
3. Marlon Brando- On the Waterfront
4. Paul Newman- Cat on a Hot Tin Roof
5. Jack Lemmon- The Apartment
6. Henry Fonda- Once Upon a Time in the West
7. James Dean- East of Eden
8. Jack Nicholson- One Flew Over the Cuckoo's Nest
9. James Stewart- Mr. Smith Goes to Washington
10. Samuel L. JAckson- Pulp Fiction