When I was younger I read 'The Well of Loneliness' by Radclyffe Hall, more than once; the scene where Stephen has to euthanise her horse, Rafferty, the words she says to him and he 'says' to her never failed to have me in bits and just thinking about it now has me welling up.
I am often in tears because of situations characters experience in books, film and TV.
In sympathy with a couple of instances mentioned by others:- Ginger in Black Beauty (more than Ginger but her particularly); Sidney Carton in A Tale of Two Cities.
Intrigued by Katherine, Anya Seaton, mentioned by Susan. I read something by her when I was a youngter, I will try and find it because if it impressed Susan it must be good.
Various scenes from 'The Hour' film.
I was very emotional in the film, 'Gandhi'.
Owl: - I am a terminally incurable sentimental old git.
Me too.
Anything involving children and animals - (not excluding adults).