It may seem strange to you, but my favorite love story movie is As Good as it Gets (1997)
It stars Jack Nicholson, Helen Hunt and Greg Kinnear and starts out with both Nicholson and Hunt living miserable lives for different reasons. Eventually, it dawns on them that in order to be happy, what they need most is each other.
I know there are much more popular films and maybe even films with better stories. But no other film has ever gotten to me like this one did.