It really depends what type of film you're looking for. You can find Cagney as a dancer or a gangster or in all sorts of roles.
I'll try to give you a little info about his famous movies mixed with some background info about his real life :
Cagney actually started as dancer/singer (someone in his neighborhood told him thats a good way for easy money)- he actually always wanted to be a farmer, and he became one finally, using the money he got from the movies.
His first theatrical role was a Drug Queen (no kidding!)
His big break on cinema came with The Public Enemy in 1931,and since then he was the ruthless gangster ever seen on cinema. The Public Enemy is one of the movies where real machine guns were used during filming.
Cagney was also known for improvising and so he came up with the idea to smash a grapefruit in Mae Clarke's face when they sit around the table.(of cousre he asked her permission first
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This is also the most famous scene from this movie.
He appeared in several roles co-starring Pat O'brien who was the opposite nice guy. (in real life it was the other way around- Pat was more outgoing than Cagney). The most famous movie of them together was Angels with dirty faces in 1938. The ending scene of this movie is often regarded as one of the scenes that changed the face of cinema forever.
Cagney was all over the media when he was accused of being a communist. He and his brother decided to come up with the most patriotic movie they can to clear all the accusations once and for all.The result was 'Yankee Doodle Dandy'.
Cganey always wanted a big movie to show his dancing skills and Yankee Doodle was it."Footlight Parade" in 1933 was a successful musical but it didnt help to get rid of his gangster image which he wanted to get rid of.
No matter how small he was,when Yankee Doodle came out in 1942 he showed the world once again what an excellent dancer he was. Yankee Doodle Dandy is not just a great musical, you also have to appreciate the quality of the dramatic scenes. Most notably, the scene with his father,where Cagney is crying. He won his only oscar for this movie.
In 1949, Cagney reprised his gangster role in White Heat. He called it "just another gangster movie" but nevertheless he gave such an outstanding performance,this time as a gang leader who's right hand is no other than his mom. "Top of the world, son" (check my location
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An intresting comparison to the comic book/animated series Lucky Luke. Lucky's enemies are the Dalton brothers and their boss is no other than their mother...Ma Dalton.
Check out Cagney's ma in White Heat and check out Ma Dalton in lucky luke and tell me what you think
The movie White Heat also features some technical police methods never seen on film before.
Once again, Cagney improvised with Virginia Mayo when he asked her permission to push her off the chair she was standing on so she would fall on the bed.
Most famous scene however is when he surprises with a gun coming out of a...(ok,I wont spoil it,just watch it!)
My sig quote is from Taxi! (1932) ,another great movie in which he delivered his most famous quote thats going to hunt him forever. However it was misquoted as "You dirty rat".
Cagney,while receiving a lifetime Achievement Award in 1974 set the record straight: "I never said 'You dirty rat!' My line was 'Judy, Judy, Judy!'"
What are his best films?