I've not personally fallen in love with a game character, but I do get very invested in on-screen romances, in films, television, books and videogames.
This means that in Bioware role-players, I get really caught up in my character's love story. I was heartbroken when Shepard and Liara were torn apart and I wanted to key Alistair's car when he left me for the throne in Dragon Age Origins.