1. Improved visibility
This is an awesome question and / or it has an awesome answer and I wish to increase its visibility to the community. (Please add 'feature request, nasty bug, etc' for the Meta sites).
2. Request for updated answers
The current answer(s) are considered out of date and require revision given recent changes in technology, software, etc.
3. Reward an existing contribution
Given an excellent answer, I wish to provide a bounty to thank the user for going above and beyond in their effort to make a quality contribution here.
4. Request for improved detail: .....
I feel that the current answers are lacking detail in one or more specific ways. I think the user should get a small amount of space to say something like:
- Please add authoritative references
- The answerers neglected to note that I said X.
- Could you provide a screen shot with your answer?
5. Other: ..........
For those many reasons which we can't cover, please select this option and explain in 250 characters why you've chosen to offer a bounty on this question.
Muddled Other Musings:
If the user can provide a description with their bounty category, then this text would have to be editable to avoid problems of vulgarity, typos, etc. Perhaps this could be along the lines of the 20K tag wiki edit privilege?
I personally don't like the idea of Could I have a solution in Java instead of C++? as I think this should be a separate question entirely. The ability to ask even mini-follow-up questions could easily lead to knowledge-base style posts which are a poor fit to the Q&A theme.
Lastly, I don't see the distinction for categorization only when offering a bounty on someone-else's question? Sure you can edit your own question to clarify your intent, but I'd prefer a consistent styling/presentation to this bounty system so why not force everyone to categorize their bounties?
Edit by waffles:
I just deployed bounty reasons based on the feedback here:

We are open to improving and amending the list, just post new meta questions if you think we need to (so we can make sense of it)