Here’s a list of what I think are some of the best Irish-themed movies for St. Patrick’s Day:
The Quiet Man (1952)
John Ford’s love song to Ireland. Its cast includes most of the members of the Ford repertory company (John Wayne, Ward Bond, Maureen O’Hara, his son-in-law Ken Curtis, his brother Seamus, etc.).
Top O’ the Morning (1949)
A charming romantic comedy vehicle for Bing Crosby. I presume that a Scot like Bing identified as Irish because of his Irish-American mother—ethnic identity tends to run in the maternal line.
Luck of the Irish (1948)
Tyrone Power visits Ireland and comes back with a leprechaun in tow.
Young Cassidy (1965)
From Sean O’Casey’s autobiography, with the lead played by Rod Taylor.
The Fighting 69th (1940)
The story of New York City’s Irish-American regiment during World War I. It features most of Hollywood’s “Irish mafia”, e.g. Jimmy Cagney, Pat O’Brien, Alan Hale, Frank McHugh, etc. They were the Rat Pack before the Rat Pack.
The Informer (1935)
John Ford’s version of the novel by Liam O’Flaherty about the Irish war of independence, starring Victor McLaglen. It has one of the most heart-rending endings in cinema. Ford won an Oscar as director and McLaglen as actor in this film.
My Left Foot (1989)
Daniel Day-Lewis does an incredible acting job as Christy Brown, a young Irishman born with cerebral palsy.
Waking Ned Devine (1998)
Ned Devine has won the Irish Lottery but Ned is dead. The movie is about the shenanigans as Ned’s neighbors attempt to claim his winnings.
The Siege of Jadotville (2016)
This movie is about an action during the UN peacekeeping mission in Congo, one of the few times (if not the only time) the Irish Army has faced combat.
This is not an encyclopedia. There are many, many Irish-themed movies, some good, some awful. Since I’m sure someone will mention them, there’s a group of horror movies with vaguely Irish themes (leprechauns, ghosts, banshees, Celtic paganism, etc.) Most are execrable.