The Glenn Miller Story (1954)

Biopic of the American band-leader, directed by Anthony Mann. 

In the title role, James Stewart seemingly makes very little effort to become the character, instead relying on his usual tics and mannerisms to carry the plot along. 

As a biopic, it’s weak. As a story in its own right, it’s reasonably entertaining but oddly childish. You learn surprisingly little about Miller’s life and career.

Anatomy of a Murder (1959)

Superb courtroom drama directed by Otto Preminger. 

James Stewart plays a brilliant but unconventional former district attorney, who acts as a defence lawyer for a suspected murder. 

There are plenty of quirky and strange characters, and dialogue is also attractively offbeat – particularly given the repeated reference to "panties". 

Every actor is remarkable, and there are memorable performances by Lee Remick (as the ambiguous Laura Manion), Ben Gazzara (as Lt. Frederick Manion) and George C. Scott (as the prosecutor Claude Dancer). Especially memorable is the judge played by Joseph N. Welch (a real-life lawyer). 

There's also an excellent soundtrack by Duke Ellington.

Vertigo (1958)

Alfred Hitchcock classic. There’s a theme of how hard life is for women when men hold all the power. Worth seeing if only for the lovely San Francisco locations with no one in them. When are cities ever that empty? Also, Kim Novak and James Stewart are spectacular in the lead roles.

Rear Window (1954)

Masterful suspense thriller by Alfred Hitchcock. Confined to his room owing to an injury, a man stares at his neighbours and uncovers a terrible crime. James Stewart and Grace Kelly are unbeatable in the lead roles. I love the slow pace and play-like feel. The luxuriously lengthy, dialogue-based scenes would never be used in modern films.