Sean - I think you meant to write what 10 films "you would most want to watch in the company of others"...with others liking them too. If so, I will have to pick the one's I think most vivid and engaging for a wider audience (so, for example, a real 'guy's picture' like Hawks' "Rio Bravo" doesn't make it.) And I assumed since you quoted the post you were thinking of Hawks and Ford.
Hawks: The Big Sleep, His Girl Friday, Red River, and (maybe not to everyone's tastes) Sergeant York, and Bringing Up Baby.
Ford: The Searchers, Stagecoach, The Quiet Man, The Grapes of Wrath, Young Mr Lincoln, My Darling Clementine, Mister Roberts, and (maybe not to everyone's tastes) The Man Who Shot Liberty Valance.
Okay, if I had to limit them to 10:
The Searchers
The Big Sleep
Red River
His Girl Friday
Stagecoach
The Grapes of Wrath
Sergeant York
The Quiet Man
My Darling Clementine
Mister Roberts
Stars, like great golf holes, are important, eh? John Wayne, Montgomery Clift, Henry Fonda, Humphrey Bogart, Cary Grant, Gary Cooper.
Also, I don't think TD is like Frank Capra (though he might be) -- but if I said Frank Capra I could've picked 8 must-see-by-all films just from him. An outstanding career!
It Happened One Night
Mr. Deeds Goes to Town
Lost Horizon
You Can't Take It With You
Mr. Smith Goes to Washington
Meet John Doe
Arsenic and Old Lace
It's a Wonderful Life
Funny, it strikes me that when you said that others had to like the films too, I automatically cut out some of my favourites by some of the best directors, e.g.
Francis Coppola - The Conversation, Apocalypse Now, (of course) Godfather I and Godfather II
Martin Scorcese - Mean Streets, Ranging Bull, Taxi Driver
John Cassavetes - Killing of a Chinese Bookie, Husbands, Women Under the Influence
Sam Peckinpah - Ride the High Country, The Wild Bunch