Aishiteru, definitely, though it's not a love story, but it's one of my favourites. I cried every single episode, it's genius!
You could also try some films, like the film version of 1 litre of tears, boku no hatsukoi wa kimi nu sasagu and Tada kimi wo aishiteru.
Although I don't know if they're really exactly what your looking for, these are quite tragic love story films as well: Time Traveller, Raiou, Tokyo Girl.
Anyway, I hope there's something you like in here! Have fun! ;)