For this exercise, I'm ignoring war or spy movies* - it's amazing how much of that stuff Americans are involved in all over the world - but Carol Reed's post-WWII classic based on a script by Graham Green gleefully wades in at number one. Writer Holly Martins (Joseph Cotten) visits Vienna on the invitation of old friend Harry Lime, played by Orson Welles, and finds himself in a whole mess of trouble. Welles later acknowledged that the cuckoo clocks in his inimitable speech atop the ferris wheel were traditionally German, not Swiss. (*or archaeology - sorry Indy!)
2. Last Tango in Paris (1972)
Another heavyweight performance, this time from Marlon Brando as a widower in an affair with a young Parisian played by Maria Schneider. They meet flat-hunting in the posh 16th arrondissement, with its views of the double-decker Pont de Bir-Hakeim. Director Bernardo Bertolucci captures desperation and fury, all within sight of a copy of the Statue of Liberty.
3. Barcelona (1994)
Rebecca Hall and Scarlett Johansson visited in Vicky Cristina Barcelona but the hugely underappreciated Whit Stillman beat Woody Allen to the Catalan capital by some 14 years. Stillman married his Spanish wife in the city in 1980 and the American cousins at the centre of his film are smitten by the local women - 'that's one of the great things about getting involved with someone from another country, you can't take it personally,' opines one.
4. Before Sunrise (1995)
In the mid-90s, director Richard Linklater had actors Ethan Hawke and Julie Delpy meet interrailing and spend the night together. Nine years later they were at it again, this time in Paris, where Hawke's character is on a book tour in Before Sunset. Lovely, and rather warming to a certain generation.
5. The Talented Mr Ripley (1999)
Perhaps a closet homosexual with definite fantastical and possibly psychopathic leanings, Tom Ripley (Matt Damon) falls under the spell of spoilt, rich Dickie Greenleaf (Jude Law) and, crucially, Greenleaf's playboy lifestyle. Italy's beaches and cities have rarely looked more inviting than in Anthony Minghella's adaptation of Patricia Highsmith's psychological thriller.
6. Roman Holiday (1953)
A generation before, Gregory Peck and Audrey Hepburn were injecting some star charisma into William Wyler's otherwise underpowered comedy romance. The couple pack in all of Rome's sights - who can forget the scene at the Bocca della Verità?
7. Frantic (1988)
Gene Kelly's Technicolor experience as An American in Paris (1951) could hardly have been more different from that of poor Harrison Ford, who finds himself thrown into the French capital's darkest spots when his wife goes missing. Roman Polanski controls the tension superbly, adding Emmanuelle Seigner as an accomplice for good measure.
8. 9 Songs (2004)
While many of these films pit Americans as fish out of water, here young student Margo Stilley wraps her legs round geologist Kieran O'Brien in a musical and sexual journey through a nine-month relationship in London. More here.
9. The Portrait of a Lady (1996)
This post was inspired by a Guardian article about literary Americans abroad that left out Arthur Phillips' Prague, which cheesed me off, but I could hardly omit Henry James, could I? Hal Hartley regular Martin Donovan joins a stellar cast, including John Malkovich and Nicole Kidman at her best as American heiress Isabel Archer touring Europe.
10. Lost in Translation (2003)
I was stuck between this and Paul Bowles adaptation The Sheltering Sky (1990) for the final spot, but we've already got Bertolucci so in come odd couple Scarlett Johansson and Bill Murray. Director Sofia Coppola overdid the alienation in her last, Somewhere, but here Tokyo steals the limelight, full as it is of crazy Japanese-speaking Japanese doing crazy Japanese things.