Question: How can I move just one email within a conversation (a response from one person within a conversation for example) into a label/folder without moving the entire conversation?

Answer: 
You can't, really. When you're looking at the conversation it shows all the labels on all the messages.

The only way to *really* do that is to turn off conversation mode, but that's like using TNT to kill a fly.

One hack-y thing you could do is forward the message to yourself (and be sure to change the subject line). Then label that forwarded message as you like.

See also:

* [How do I split conversations in Gmail?](https://webapps.stackexchange.com/questions/4175/how-do-i-split-conversations-in-gmail)
* [Can I archive only certain messages within a conversation?](https://webapps.stackexchange.com/questions/12064/can-i-archive-only-certain-messages-within-a-conversation)
So far I have not found a way to do this, very annoying especially when I get emails with the same subject that I don't want to be threaded.

The only way I have found out how to do this is use an IMAP client (e.g. Mail app on iPhone) and then you can move any emails you like, threaded or not.