One thing about me is that I am interested in constructive critique of my writing. I don't expect people to necessarily bother with it, since it's a lot of work and often unappreciated, but I do appreciate when it's given.
Of course, not all criticism is constructive--if someone just hates the entire direction of a story, they can still come up with a reasonably detailed critique, but that doesn't make that critique constructive. In my opinion, it's better to reserve non-constructive critique for situations where the author isn't being addressed directly. I don't think it's necessarily valueless, but I also don't think it has a place in fanfiction comments.
Constructive critique offers the possibility of fixing the problem(s) the critiquer takes issue with. If it's something like 'this entire story is boring and I hate it' or 'I think you should cut out the main character' that's not something I view as constructive.
On the other hand, if it's something like 'I really like this story but I don't like the direction it's taken in the latest chapter because x,y, and z' or 'I spotted these grammatical and spelling errors' or 'hey could you write what's happening with character b now? They're my favorite and we haven't seen them in a few chapters'. Then that's constructive criticism. Even if I don't decide to follow up on it, those types of things are not an unreasonable request.
I also do try to incorporate feedback on my story whenever possible. After all, even though my primary purpose is to write something I enjoy, I wouldn't bother putting it online if I didn't hope to write something other people could enjoy too.
