Community wiki is not a rep waiver
I've mentioned that from time to time in the past.
Community wiki doesn't just mean that you cannot earn rep from a post. Yes, it does have that side effect, but the community wiki option is for posts that can be edited by anyone without worrying about post ownership. Edits that are usually frowned upon – and rejected when suggested – such as editing the code in an answer, are not only tolerated but welcomed in the case of a community wiki post. Making your answer community wiki means that everyone should feel free to improve the post; even users with as little 100 reputation won't have to get their edits approved.
This feature was introduced back when Stack Overflow was very different. List-of questions have been off-topic for a long time now, suggested edits have been implemented, and community wiki rarely makes sense nowadays. And while community wiki works as a rep waiver, it shouldn't be used as one. Should the community wiki police be shut down? is a post on Mother Meta from 2009, yet I still see the occasional comment (or flag) stating that a post should be community wiki for non-wiki reasons.
I improve someone else's answer and offer the changes to them in a comment. However, they refuse to include it for whatever reason (usually because they find that the change is too substantial), so I post the new solution myself.
Just post it yourself, but don't make it a wiki. It is still your post. It's based on someone else's, but you can (and should) address that in the post, giving credit where credit is due. If others don't think the improvement is interesting enough, they won't upvote. Personally, I care much more about upvotes than reputation.
I port someone else's answer to another language and post it myself.
See above. The implementation is your work.
Someone ports my answer to another language and offers to let me post it.
The comment suggests that the poster is OK with you posting the port, so either do it – and, of course, credit him – or politely decline and let him post the answer himself.
Someone suggests improvements to my answer and I include them.
I think that hasn't even come up in the wild. I've edited countless suggestions into my posts (again, with credit) without making them community wiki.
Several users solve a challenge together in chat. One of them posts it.
That's the closest one to the intended use of community wikis. Still, this post is the work of a few collaborators, not the entire community, so even in this case, I wouldn't make it a wiki.
I've found a competitive solution to a challenge elsewhere on the internet and would like to post it for completeness' sake (giving due credit).
That's done on other SE sites all the time, and nobody marks these answers as community wiki, even if they contain little more than a quote from a blog post.
You may not have written the code yourself, but finding it can be just as difficult. Also, this is only slightly different from finding a language that happens to have the solution as a built-in, or from using a freely available BF generator to create a constant output.
We've discussed that before and I agree with the reached consensus.
The generic tips for golfing in X posts have a wiki-like list-of nature, but the answers should preferably be limited to one tip per post (so the good tips rise to the top when sorting by votes), meaning that they aren't collaboration efforts and should therefore not be community wiki.
Making the questions themselves community wiki might make sense, but it's not worth the trouble since this would automatically wiki all newly posted answers, and thus require moderator intervention to unwiki them.
So when does community wiki make sense?
99 times out of 100, it doesn't. Off the top of my head, one could create an answer to Showcase your language one vote at a time where others should feel free to add snippets of their own.
Can I make my answer community wiki
Of course! It's your answer. Before you wiki it, anyway...
Note that by making your answer community wiki, you essentially give up ownership and invite the entire community to improve it.
Finally, if you have posted a community wiki answer for whatever reason and want to unwiki it, please feel free to flag it for moderator attention.