Alright, you want romance movies that don't follow the norm and are great? I can think of a few that my wife introduced to me and now I've grown fond of:
Princess Bride: If you've seen the story of Wesley and Buttercup you haven't forgot it. What more could you ask of a romantic movie? Swordplay, The humor of Wallace Shawn (Vizzini), Cary Elwes as a badass, Andre the Giant! and R.O.U.S. (watch the movie).
Moulin Rouge: Obi-Wan sings and dances? That's right, Ewan McGregor and a cast that includes Nicole Kidman and John Leguizamo do renditions of popular songs as Ewan fights for Nicole's love. One of my wife's favorites and it includes a medley that has "All You Need is Love" - The Beatles, "Pride" (In the Name of Love) - U2, ""Silly Love Songs" - Paul McCartney, "Your Song" - Elton John and "Heroes" - David Bowie among others.
Casablanca: Maybe the most quoted romance movie of all time. "Here's Looking at you kid" and "If you don't get in that plane you'll regret it. Maybe not today, maybe not tomorrow, but soon and for the rest of your life." Great movie, if you don't mind balck and white and a true classic.
Paris When It Sizzles & Breakfast at Tiffany's: Audrey Hepburn at her finest. "Paris" is the story of a screenplay writer trying to finish a script that he promised his bosses was done weeks earlier, in two days and his typist (Hepburn) who helps come up with a twist on a twist on a twist (Once again, watch the movie). "Breakfast" on the other hand is about a Prostitute (although it's never really confirmed it's quite obvious) and a gigolo (is confirmed) falling love even though Hepburn spurns him at every turn.
Singing in the Rain: The second musical on my list (after Moulin Rouge) is far and away my favorite on this list. It's about a movie studio during the "silent film" era which is in trouble after the debut of "talkies" (modern movies). It has a couple of boring parts but the dancing by Gene Kelly and Donald O'Connor is amazing. "Make Em' Laugh" by Donald O'Connor was recently re-done by Joseph Gordon-Levitt on SNL and it has plenty of other great songs as well: "Moses Supposes", "Good Morning", "Dream of You" and of course the title song "Singing In the Rain" which Gene Kelly performed with a 103 degree fever. Gene Kelly may have been a douche (he insulted Debbie Reynold's dancing, his love interest in the movie crazy enough) but he not only danced and sang but he helped with the choreography and convinced Donald to do the running wall back flip that is probably the most celebrated dance moment in the movie.
There's a couple for you to watch the trailer at least.