Personally, if I ask for a crit of course I really want to hear if the reader likes it, but more importantly, I want to know if they get what I'm saying and if they would want to read it in print. I appreciate grammar corrections and so on but it's whether it works as a story that's most vital. I don't mind if the reader picks faults but I do mind if they don't give me reasons for what they say. Personal taste isn't really a useful reason for slamming something so if that's all a critiquer has to offer I'm not going to take any notice. But, if they tell me there's a fault in the structure or a character is unconvincing and why, I will certainly pay attention.
The thing is critiquing is always personal to a degree. We all have our likes and dislikes and obviously this will influence how we read a piece but we should be able to rise above this and use our analytical processes as well. The other things I always expect are politeness, honesty and a degree of kindness. This doesn't mean telling me this piece is wonderful - I'm not silly enough to believe everything I write is perfect - but you can point out what works and doesn't work without being offensive.
When I give writing workshops on how to critique I always tell my students that I've never yet read a piece which doesn't have at least one positive point even if the bulk is a total disaster. That positive aspect should be acknowledged and then the rest can be analysed sympathetically. If I start a crit by saying something like the idea is interesting or provocative (assuming it is, of course) then I can move on to what doesn't work for me and why. It's quite reasonable to say that I'm not the target market for it but that doesn't disqualify me from commenting on the way the story is put together, for instance.
The other thing for a writer to remember is that a critique is only one person's opinion and you don't have to agree with it. That said, I've never yet had a crit that I haven't learned something from. I have a kind of mantra when I send something out for a crit for when it comes back. It is that if one person makes a comment I should look at it carefully and decide whether I agree with it or not. If two people make similar comments alarm bells should start to ring and I need to put it away for a while then come back and reassess, but if more than two agree, no matter how much I love it, they are probably right. In that case I put it aside and work on something completely different and then come back and reread the comments before I do a complete rewrite.
I'm fairly unusual, I suspect, because I really like having my work critted. It certainly can shake your confidence and be painful but the gain is worth the pain.