I don't agree with the "it's ultimately their decision" comment. That's a little too absolute for me. There are different mental states people can be in... some characteristic of their normal personality and some are transient (ie. drunk, depression, etc) current states. I'm not saying that I'd stop everyone absolutely, but that I would take each case on a case to case basis. I can't fathom a viable scenario where I'd let someone kill themselves ( I struggle with assisted suicide for patients who are degenerating and writhing in permanent incapacitating pain). Philosophical possibility is not realistic probability. I'm not saying it doesn't exist, but I don't think I've heard of any legitimate (or otherwise) instance where someone who his just perfectly fine and not depressed (or what have you) who just up and said... "lala la la la... I think I'm going to kill myself today" I'm sure someone somewhere has done it before, but I'm going to exclude that scenario from the ones I'm discussing.
I go to parties from time to time, but I don't drink. I'm usually the dd or just a people watcher. I have friends that would never do sober what they consider doing drunk (and sometimes end up doing... right there in the middle of everyone). Well... at least the humiliation and disgust on their face that shows up after they're told what they did seems sincere. Some people have argued before that alcohol doesn't change people's personalities or what they'll do. Everyone has the potential to respond to things like that differently and what you're saying isn't always true. According to some, I'd be in the wrong to stop an inebriated close friend from doing something stupid when I know they wouldn't do it while not drunk.
The only people I've known that have killed themselves or performed self mutilation have had problems with depression and other such issues. If I see someone about to kill themselves, I'm going to assume that they're going to do something they wouldn't normally do outside of their assumed depression/problems and I am going to stop them. I believe that the fact different drugs like acutane come with the warning label of "it can potentially alter your brain chemistry and make you depressed to the point of committing suicide" shows that depression can be (and in my experience usually is) a temporary/transient brain state that can lead to severely harmful decisions on the depressed person's part that they wouldn't otherwise decide to do.
I has a mental game I'd like to plays... so here it is. What about the idea of indoctrination of said suicidal person into not killing themselves? Maybe that's not the right word, but the idea is pretty much the same. You stop a suicidal person and then you convince them by either logic or somehow forcibly reconstructing the person's thought processes into not wanting to kill themselves. Some say that breaking someone down and making them believe what you want them to so as to further your own agendas is absolutely bad... but what would you who would have let them kill themselves do then? Would you change their new opinions and ideas back to the old? Would you "fix" them so as to let them kill themselves? ...or would you just say that it's ultimately their decision and that their new decision (indoctrinated or not) just happens to be relatively better...but it matters not to you whether or not they actually kill themselves?
If someone is rewired to think differently, then is their new opinion and agenda just as acceptable to you as the last one you were all "well... it's their decision?" Is it bad to rewire someone to value their life more so as to keep them from killing themselves?