Apparently the fountain doesn't exist, but it's not completely fake. It was inspired by another fountain that also located in Rome, Trevi Fountain (Fontana di Trevi).
Standing 25.9 meters (85 feet) high and 19.8 meters (65 feet) wide, it took 30 years (1732-1762) to built this fountain. The order came from Pope Clementine XII, it was started by artist Nicola Salvi, but he died in 1751, with his work half-done. Giuseppe Pannini resume the job and finished it in 1762, long after the Pope died.
The central figure of the Trevi Fountain, in front of a large niche, is Neptune, god of the sea. He is riding a chariot in the shape of a shell, pulled by two sea horses. Each sea horse is guided by a Triton. One of the horses is calm and obedient, the other one restive. They symbolize the fluctuating moods of the sea. To the side are the statues of Abundance and Salubrity.
The water at the bottom of Trevi Fountain represents the sea.
A lot of people miss-interpreted that throwing coin to this fountain water will bring good luck in love, said that two coins will lead to a new romance and three will ensure either a marriage or divorce.
Actually, legend has it that you will guarantee that somehow you will find your way back to return to Rome if you throw a coin into the water. You should toss it over your shoulder with your back to the fountain.
An estimated 3,000 euros are thrown into the fountain each day. The money has been used to subsidize a supermarket for Rome's needy. However, there are regular attempts to steal coins from the fountain.
Besides When in Rome who only explicitly mentions this place, there are another movies who used Trevi Fountain in their story. One of them is Academy Awards winner Three Coins in the Fountain (1954). It tells the story of three American girls looking for romance in Rome while employed at the American Embassy.
Another movie that used this fountain is the renowned Italian film, La Dolce Vita (1960) by Fellini; on a quiet night in an almost unreal Rome, an alluring Anita Ekberg jumps into the Trevi Fountain with her clothes on and invites Marcello Mastroianni to join her.