I found that a very effective response to someone who threatened suicide if I ended the relationship was to tell him that if his life without me was going to be that bad, I respected his decision. Went around for a few days feeling that my head was going to explode, but didn't cave in to the manipulation.
I found the threat particularly vicious because my father HAD committed suicide a few years earlier - of which he was well aware - and my own anger gave me the strength to stay calm in the face of the threat.