Splash is probably the most famous mainstream mermaid movie there is. The film was released in 1984 and became the runaway romantic comedy of the year, pushing stars Tom Hanks and Daryl Hannah into the spotlight.
The plot itself is simple enough. There is a mermaid (Daryl Hannah), and there is a man (Tom Hanks). Not unlike Hans Christian Andersen's mermaid, Splash's mermaid saves her young man's life and follows him to land, but therein the similarities end. This mermaid's tail automatically turns into a pair of legs when she's dry, so her appearance on dry land comes at little cost. She is also able to win her young man within a heartbeat. The only real catches are that he doesn't she knows that she's a mermaid, she doesn't know how to tell him, and she has to return to her home by the next full moon. But really, with one thing and another, they do end up together and live happily ever after. It's sweet and fluffy, and admittedly not all that realistic, but its memorability has made it a classic.
The main reason I watched this movie when I was a kid was to see the mermaid. Daryl Hannah did an amazing job what with she was given, making it easy to believe that mermaids could exist. Considering some of the other mermaids that have appeared in the movies and on television after Splash, it makes you appreciate all the more how Daryl made swimming in a tail look effortless and realistic at the same time.
According to an interview with Daryl in the 20th Anniversary DVD, she'd been swimming like a "mermaid" (that is, with her legs tied together) ever since she was a kid, so when she was given the role of Madison, it was a dream come true, and she even swam better than the stunt women who were supposed to double for her. The only real disappointment for me about the movie is that there weren't enough underwater scenes.