Should we kill healthy people for their organs?

No, even if it did save people it would ruin the population. Basically in China murder is allowed, it's horrible hearing about things in China. I would not like that to be the same in United States and/or World Wide!

Theoretically this would be appropriate and prolong life in general. We'd have to have a 100% heartless population though. Which will never happen.
Eventually too, nobody would be healthy anymore on purpose, which would cause us to die out quicker in the long run. Probably a bad idea.

Well if your coming from a utilitaranistic view then yes, you can say you did the right thing.
This is no different from the train senario where on one track there is five people and on the second one person.

Do you pull the lever to change the trains direction and kill only one person?
Either way you go, its still murder.

For me I don't like to toy or mess with death, so not pulling the lever in my opinion saves you the guilt.

I feel that this is what has happened in history, but were part of genocides. It should be the healthy person's decision.

We shouldn't. My Identification Card states I will donate my organs when I die.

That's how it should be.

Suppose Bill is a healthy man without family or loved ones. Would it be ok painlessly to kill him if his organs would save five people, one of whom needs a heart, another a kidney, and so on? If not, why not?

No, that would not be okay. Firstly, like everyone else has said, no one is in the position to condemn an innocent man to death. Secondly, we do enough of taking from the healthy and protecting the weak.

Consider another case: you and six others are kidnapped, and the kidnapper somehow persuades you that if you shoot dead one of the other hostages, he will set the remaining five free, whereas if you do not, he will shoot all six. (Either way, he'll release you.)
Source

This is actually a tough one. When it comes down to it, either 1 person will die or 6 people will die. I'll choose the one where I shoot one to save the rest.

We shouldn't. My Identification Card states I will donate my organs when I die.

That's how it should be.

I.e. when I get sick and have to go to the hospital with a potentially terminal illness, go ahead and let me die so you can harvest my organs for the next guy.

Not sure if you're thinking about this or not.
Are you suggesting allowing assisted suicide for those unhappy and set on ending their lives In exchange for their healthy organs? Or straight up finding family-less, healthy people and cutting their life short?
I disagree with just killing for it. The suicide thing is a bit iffy also in my opinion but would help without being murder in my opinion.

Suppose Bill is a healthy man without family or loved ones. Would it be ok painlessly to kill him if his organs would save five people, one of whom needs a heart, another a kidney, and so on? If not, why not?

Consider another case: you and six others are kidnapped, and the kidnapper somehow persuades you that if you shoot dead one of the other hostages, he will set the remaining five free, whereas if you do not, he will shoot all six. (Either way, he'll release you.)
Source

I feel that if that is what Bill wants, then that is what should happen. I mean, he'd be helping people, yes, but he is a human who has a mind of his own. He deserves to make the decision.

As for this one, if I were in this situation, I honestly don't know what I would do. I mean, are any of the other people I'm with injured severely, or sick, etc?