You ask a very hard question, Ace. Both actors made many, many great films. My favorites:
Cagney:
White Heat
Public Enemy
One, Two, Three
Roaring Twenties
Mr. Roberts
(I don't think he ever made a bad film)

Bogart:
Caine Mutiny
African Queen
Treasure of the Sierra Madre
The Harder They Fall
Casablanca
Petrified Forest
High Sierra
(I don't think he ever made a bad film)

You can check if any or all of these are on DVD by visiting http://www.imdb.com