When you post work for a critique, what do you expect?
I'm not sure what I expect, as there is such a range of different critiquing styles around here, but what I hope for is an honest opinion given in a courteous manner.
What do you consider a good critique?
When I critique other people's work, I try to be as objective as possible, and I also try to get a balance bewteen positive and negative comments. If possible I will mention what did impress me as well as the parts I stumbled over. One thing I've found in critiques of my own work is that, while the negative comments are helpful in that obviously something needs addressed (whether I end up changing it or not remains to be seen, as it might just be a difference of opinion between myself and the critter, but the fact that someone got stuck on a point means I should go back and have a critical look at that section), however if the critiques only mention problems, I don't know if the critiquers don't like anything, therefore the whole project is flawed, or if they are just of the school of critiquing that doesn't go in for mentioning positives. I need to know what works as well as what doesn't in order to form a rounded view of the piece.
What makes a critique bad?
Well, rudeness and just blanket 'it sucks' goes without saying I suppose. One thing that for me makes a critique bad (and so something I try to avoid myself when reviewing) is when the critiquer makes a valid point but does so in a condescending or patronising way. For an example, if someone says to me 'your dialogue is a bit melodramatic there' I can understand that, and examples of where it's over the top help even more, but what I don't need is two paragraphs where they explain to me what 'melodramatic' means and why that's a very bad thing for writing, all in words of one syllable. I've had quite a few comments where the actual point about the text was true enough but my blood has been boiling for a long time because the critiquer spoke to me as if I was an idiot. So I always try to address writers in a respectful manner and assume some level of intelligence on their part.
Also, ones I don't find helpful are where the critiquer argues with your character's motivations or the way the story is headed. I can understand maybe 'I don't think someone in that position would react in such a way', but not 'I don't think Brannen would behave like that'. The strange thing has been that some of those comments came from readers who hadn't seen the whole book. I also had a beta reader once who told me that I shouldn't write the story as a romance, I should do it this other way and make the characters do this etc. basically changing the whole plot of the book.
What's the worst critique you have ever received?
Not sure, actually, not if by 'worst critique' you mean one that was really unhelpful as opposed to the worst, as in the writing received the most negative comments. I had one once that just compared everything I'd written to elements from movies. The basic story was of a man dabbling in the dark arts, who came a cropper because of it, having summoned up a demon-type thing, and was told from the POV of a student studying at a private school where this man taught. There was one scene where the students saw the creature climbing up the wall of the school to the master's window. It was all a bit kind of M R James in tone, or at least it was meant to be. The critiquer said that the creature just made her think of some cartoon thing, the master's servant made her think of someone in some Vincent Price movie, whole load of things like this, but didn't say whether this was meant to be good, bad or indifferent. I got the impression it was meant as a criticism, but was left a bit bewildered by the whole thing.
I'm glad this thread prompted me to remember that though as I've just thought what a good short story that section would make.
Again, not sure. I think probably one I received ages ago on a description of a battle scene, that pointed out the way to use active verbs rather than passive to make it more immediate, and that's something that's stayed with me ever since. Sounds like a really obvious point but I hadn't thought about it until then and it's been really useful in loads of different pieces of writing.
Have you ever, in retrospect, been embarrassed by your own behavior?
Every five minutes. I'm going to employ Dempsey's technique of leaving things a while before replying in future. I'm the opposite of the defensive author and I tend to take negative criticisms as an indication that I have no talent whatsoever, whether that is what the critiquer means or not. Basically I tend to put more weight onto the comment than was meant or is actually appropriate. Then I tend to get very frustrated and upset because I'm embarrassed that I posted something so bad and that people are now thinking 'God, what a crap writer she is, imagine wasting our time like that', and so on. I then realise I shouldn't have whined so much and try to explain why I reacted as I did and just end up sounding like I'm making excuses and make it worse. Really what I need to learn is to shut the hell up.
It's one of those vicious circle things. Because I have a lack of confidence in my own work, I'm not able to stand up for myself and believe in the piece even in the face of negative criticism and tend to react badly, but because I've had so many negative comments over the past year or so, I lack confidence in my own work.
I believe my first critter got a migraine (probably required brain surgery) after reading my first draft. Boy, did it suck! On a serious note, I benefited the most. 
