Walter Brennan. He was the go-to guy whenever a cussed old western sidekick, comic hayseed, or shrewd cowboy villain was needed. He also stole more than his regulation share of scenes from the lead guy.
Definitely going to go with Gary Oldman, Alan Tudyk takes second.
Needle-Nose Ned? Ned the Head?
They’ve had lead roles, but in small movies and are still essentially character actors:
More love for Harry Dean Stanton, Gary Oldman and Strother Martin.
For the ladies, Margaret Dumont, Holland Taylor (Evelyn Harper on 2.5 Men), and the late Nancy Walker.
No need to hold it against him.
“Often referred to as an actor’s actor, his work as a character actor has earned him the nickname of Human Chameleon.” --Wiki biography
I miss not seeing John Cazale around any more, he was always fascinating to watch. I just read his Wiki, and he was only in a half-dozen films, and died at 42.
Another vote for William H. Macy. I will see anything that has him in the cast list.
I have all the love in the world for David Morse
Wilhelm Scream.
Even back in 1971, In what is now a sort of cult hot rod flick staring James Taylor and Dennis Wilson. There was a brief part about a gay hitchhiker, who?
Harry Dean Stanton. Billed as H.D. Stanton.
And it was just a great little odd moment, in a great little odd film.
“Two Lane Blacktop.”
One of my favorites. I still say Warren Oates should have got an Oscar.
Yeah, he’s been in a LOT of movies!
Ian Holm: his IMDB entry.
(There are others I would have mentioned, but they graduated to leading roles after many years of supporting roles, so they’re DQ’d for the purposes of this thread.)
Timothy Carey for the win. Walter Brennan, Harry Dean Stanton, and Elisha Cook, Jr. for honorable mentions. (No offense, gang!)
What about Denis O’Hare? For the longest time, I knew his face but not his name. He was in lots of Law & Order shows and had supporting roles in other films and TV shows.
You have good taste. This is without a doubt one of the best movies ever made. It’s a minimalist masterpiece. Warren Oates played such an amazingly good drifter, he had a story for everybody, and in the end it came all the way back around.
Highly recommended movie. I thought I was one of the 20 or so people left on Earth that actually liked it. It’s hard to believe that there are two of us here.
Better make that 3 of us. I own it on DVD.
But James Hong isn’t just the “generic Asian actor.” He’s the generic Asian high-class authority-figure actor. He always seems to turn up as a businessman, politician, diplomat, mob boss or master-of-something. Need a guy to play Cassandra’s stuffy dad in Wayne’s World 2? James Hong is your guy. He’s the Chinese James Rebhorn.
And of course, there’s Tzi Ma, the Bill Pullman to Hong’s Bill Paxton. Or maybe it’s the other way around. He’s not quite as ubiquitous or as typecast as Hong, but he’s the other Asian go-to guy for the same types of roles.
The Will Patton to Hong’s Bill Pullman and Ma’s Bill Paxton (or maybe its the other way around) is Al Leong. If you need crazy violent Asian guy with a great mustache, Al Leong is going to be your first choice. Genghis Khan? Check!
And let’s not forget B. D. Wong, who is the…well, I’m out of Bill/Will P___ns. He has the little delicate Asian guy market cornered.
Approximately 50% of all Hollywood roles for Asian men are filled by either Hong, Ma, Leong, or Wong.
Dwight Frye
Edgar Buchanan
John Carradine
Tim Blake Nelson
Charles Durning
You forgot his roles as Booger’s mentor in “Revenge of the Nerds, Nerds in Paradise”, and Mike Meyer’s future father-in-law in “Wayne’s World 2” 
B.D. Wong is the Billy Zane to Hong’s Bill Pullman to Ma’s Bill Paxton.
They both have played effeminates (Father of the Bride, The Freshman, Tombstone).
They both have played badasses (Executive Decision, The Phantom, Posse).