Bicycle Thief (1948)
Directed by the Fascist-era matinee idol Vittorio De Sica from a script by veteran screenwriter Cesare Zavattini, said by the Village Voice to be the most universally praised movie produced anywhere on planet earth during the first decade after World War II. A workman spends a whole day looking in vain in the streets of Rome for the bicycle someone has stolen from him.
(added by Doug Mink)

Breaking Away (1979)
Local cyclist in a small town (townies aka “cutters”), lives, eats, and breathes cycling and everything else Italian, comes of age in a race against college kids. Based on Dave Blaze, and his experiences at Indiana University and the Little 500.

American Flyers (1985)
Two brothers, a former National caliber rider (Kevin Costner) and his enthusiastic ‘newbee’ brother, take an adventure to the ‘Hell of the West’ (aka Coors Classic) stage race. Lots of good ‘Coors Classic’ footage in this one, even Eddy Merckx makes an appearance.

Quicksilver
Trials and tribulations in the tough world of bicycle messengers in San Francisco. Stars Kevin Bacon, and Nelson Vails, with great stunt shots of cycling (often in illegal ways) in traffic.

My personal favorites are Breaking Away and American Flyers.

Check out more bicycle movies at Mass Bike