Like Quinlor said, it really depends on the person and the circumstances, especially with respect to the possibility of healing.
If someone is upset by a relationship ending, while I can understand the pain, I also understand that their perspective is skewed by the present pain which could very well be a passing one. I'd intervene because I'd believe it is something their future self would want.
Also, if someone told me they are about to pull the trigger, jump, just swallowed a bunch of pills, I would interpret that as a cry for help and would (and have) intervened. If someone really wants to kill themselves, they're not going to communicate that to me at the last moment and expect me to just let it go at that.
However, if someone has a debilitating and chronic or terminal illness which made living burdensome with no realistic possibility of improvement (intense pain, ALS, e.g.), I would support their decision, celebrate their life. If they wanted to go to Dignitas, I'd go with them if I could afford to do it.
I'm sure I'll get a lot of flack for this, but I am being honest.