Yes, after a tennis match once. He was an asshole who acted horribly on the court.
I’m sure ZPGZealot would have a story or two to tell…
Arrestees / detainees.
It’s just policy.
I said, “Good day!”
I’ve avoided people in handshake lines after sporting events on rare occasions.
I’ve declined when dealing with a cold as well. Honestly, I’d rather not shake hands with anyone.
Greg Hawkes of The Cars does not shake hands, preferring the hands-clasped-together namaste greeting used by Hindus and Buddhists. Really nice, and astonishingly talented, guy
Sometimes I just can’t stand to be touched - by anyone. Not even a hand shake. Especially after a really bad flashback. I make sure that the other person knows they are not at fault
I have refused to shake the hand of a boss who fired me to save his own ass politically, it was the cut direct. I walked away leaving him with his hand out and looking foolish in front of witnesses. He deserved it. Other than that, the only times I have refused are when my hands are dirty for some reason and I explain the situation. For the record, I have shaken hands with people I have known to be felons, babykillers, wifekillers, kidnappers and other criminaLs. This is because of my work as a nurse and as a Sheriff’s secretary in a small jail.
My ungloved hand does not touch the hand of a man unrelated to me unless I am performing a medical procedure (it’s happened a few times when I was changing someone’s bandages). Any man who has a problem with that immediately goes on my asshole list as deserving scorn and extra scrutiny anytime we’re in an isolated area. I will shake hands with another woman and probably have shaken hands with a few transsexuals and drag queens who were very convincing. Oddly enough the only one I know about was a drag queen who came up and apologized to me after a show when he realized I had inadvertantly broken a cultural taboo. As an aside, I tend to think of people who shake hands at greetings as being shallow. For me, a handshake is a gesture in front of witnesses to signal an agreement has been made. People I do busines with know that a handshake with me is more solid than a contract hammered out by a team of lawyers. Naturally, one doesn’t make such a gesture during an introduction.
A few times, with men I disliked for one reason or another. I did it on the grounds that the woman extends her hand and indicates if she will shake, it is not up to the man to decide she will shake hands.
I know it is old school manners, but I really dislike pushy men.
I don’t think I’ve ever refused to shake someone’s hand out of principle but there are a few who got a particularly hard squeeze and a smug grin.
Not that I didn’t want to but based on how I was treated by the receiving nurse who took my blood pressure over my sweather, when the doctor came in the room and presented his hand to mine and introduce himself. I didn’t reciprocate instead offered " I think I have shingles you probably don’t want to shake my hand."
He said " shingles isn’t as contagious as people think, how about a fist bump instead ?" Cool doctor.
Yup you have shingles.
Orthodox Jewish women will refuse to shake hands with a man, IIRC.
Aaand there we go… 
Once when I was maybe 17 or 18 years old, I refused to shake my Uncle’s hand after we had an argument over how racist he is.
I worked for a character who had a string of work related insulting jokes. “Civil Engineer” was an example. I’ve seen him run out of an engineering office for making a joke about insurance liability.
I also saw him quietly cut by a catholic priest – hand up to scratch his ear instead of shaking – for making a joke about little boys. He had an insult for everyone.
An acquiantance of mine appears to suffer from Asperger’s Syndrome. One of his more annoying traits is his constantly wiping his nose with his bare hands. This wouldn’t be a problem if he didn’t always insist on shaking hands upon meeting at a restaurant we both frequent. I usually comply, and sneak away and wash my hands immediately. But if I’m eating, I will decline, pointing to the food.
He was a governor. I’d rather not say who.
I have a similar opinion on any Head of State, I’ve only shaken hands with two Presidents at rope lines and both were Presidents I liked (Reagan/Bush I) but if somehow I was in a scenario where President Obama extended his hand I’d shake it. I don’t really think it’s appropriate to show disrespect to a Head of State. I’m fine with protesting and all the other acts of civil society, but I think personal disrespect (this includes shouting rude things, etc) crosses a line for me. I think for example burning in effigy is an age old political expression and am fine with that, but if the President is physically present I think it’s low class to yell insults/obscenities at him or etc.
I’d feel the same way about the Queen of the UK or etc…less certain on Prime Ministers and such, they’re more like civil servants in chief than holders of a respected office.
Pretty rare, but it has happened.
Boss who completely screwed me over, lied to his bosses about it and fired me, then offered to shake my hand in parting. Oh no. Not happening.
I dimly recall a long time ago in my younger days, someone I’d never met deciding to have some fun insulting the fuck out of me at a party for no discernable reason, then finding out that I was friends with people he was trying to impress and get in tight with. Coming back to me later, sticking out his hand and saying “no hard feelings” (note: NOT apologizing, just saying ‘no hard feelings’) I turned and walked away without a word, shaking my head.