Christina Ricci and Dennis Hopper play chess
Dennis Hopper, Kate Beckinsale and Christina Ricci star in the new 30-second commercials, which have been filmed in black-and-white to promote the chain's summer range.
The store is known for its simple ads starring big names, with Aerosmith, Juliette Lewis and Shaggy among those to have featured in the past.
Roman Coppola, Francis Ford Coppola's son, has directed the third of the new ads, which will be shown in the United States from the end of April.
Crowe, who made Jerry Maguire and Almost Famous, has entered the world of TV advertising for the first time with the clip, which features Beckinsale and Lord of the Rings star Orlando Bloom as a strolling couple.
Hopper and Ricci are seen lounging by the side of a pool and playing chess in the ad directed by the Coen brothers.
The brothers are best-known for their off-beat films like O Brother, Where Art Thou? and Fargo.
The final clip, by Coppola, sees a group of friends riding on bicycles through empty streets.
The campaign was co-ordinated by Lisa Prisco, who tried to make the commercials feel like short films.
"Lisa, Cameron Crowe, the Coen brothers and Roman Coppola have created a campaign that speaks to summer moments in simple, classic Gap style," Gap executive Peter Hempel said.
The ads will be seen in the United States from 28 April, and will also be screened in the UK and Canada.
The most recent campaign saw music stars including Macy Gray, Alanis Morissette and Seal sing sections of Supertramp's Give a Little Bit.