What programs do the writers here use to plan out their conversation trees? I've tried Word, but it just ends up a mess of formating to make it clear what part happens after what, and what choices of responses belong to which question. Excel didn't work so well either. At the moment the best thing I have found for planning out my conversation trees is the one included in the Neverwinter Nights Aurora toolset. Are there any stand-alone programs out their with the similar functionality?

Your needs are not very clear.
For editing in-game text every game needs custom tools (typically a special text format with noninteractive processing), while for mere planning diagrams and notes on paper and whiteboards are usually the most convenient technology.
Using generic software, or software borrowed from a different game, to plan game conversations and texts is vastly slower and more difficult than using pencil and paper and not directly useful as a prototype.

I'm not looking for something to use as a prototype, or that I can shoehorn into a game.

I have spent the past few months coding my game engine, and am about ready to grind through my teeth if I boot up Visual Studio any time soon.
So I figured I would take a break from coding and get some of the dialogue for my game written.

I haven't written the code to handle converstations in my game yet.

So basically I was looking for any kind of program that would let me to the busy work of writing the story and managing the various branching conversations.
If I write the dialogue onto pieces of paper or whiteboards, I will just have to transcribe it onto the computer eventually anyway. I was looking for a tidier way of doing what you mention, and on a computer.
Possibly something that saved each fragment of the conversation tree into a sensibly named or coded text file.



If a program for drafting conversation trees doesn't exist, then I will just keep on using Aurora and copy and paste the text from Aurora into text files when I write the dialogue code for my game.

Perhaps TreePad or The Literary Machine will fit your needs.