From the Super Mario Wiki
The Trevi Fountain (in Italian: Fontana di Trevi) is a famous landmark in Rome, built in 1762. It is said to ensure anyone who throws coins into the fountain a return to the city. The Trevi Fountain appears in Mario is Missing! as one of the landmarks that are attacked by Koopa Troopas and that Luigi subsequently visits in Rome. It is closed because the Koopa Troopas stole the fountain's Coins, and it cannot reopen until Luigi returns them. After bringing them to the information booth and proving their authenticity (done by answering various questions, listed below), he is given $1500 as a reward.
Legend says that if a visitor tosses coins over his shoulder into the Trevi Fountain he will one day return to Rome. The Trevi Fountain is one of the best known landmarks in Rome because of its fable, but also because of its fancy carvings. The fountain was shown in a 1954 movie, 'Three Coins in the Fountain.'