Let's start with a funny quote since the rest of this post isn't very funny! "I think G-d is a goy. A mix of a girl and a boy." - a 3rd grader
And a quick definition to get us all on the same page! A connotation is "a subjective cultural and/or emotional coloration" of a word. You have the denotation, which is the actual dictionary definition, but connotation is all the "baggage" of a word. For instance, ideas and emotions instinctively pop into your head when you hear the word "mother" or "spider." Those are the connotations of those words.
Until I started "really" running in orthodox circles (remember that I had three years of lax orthodox affiliation when I first began my conversion process!), I can't remember hearing the word "goy" more than a handful of times, and always from people I would classify as elderly. Of course, you read it more often. I imagined that "goy" was like the terms people use for racial groups (aka, you can almost always tell how old the person is who's speaking!). I also thought goy had a negative connotation to it (like "shiksa" - don't even get me started on that awful word! Don't say it!). But then again, because of the way I heard people say it, I used to think "chareidi" was also a negative word! (A commenter on here cleared that up for me!)
Of course, my understanding is that the word "goy" itself is neutral and simply a descriptor, just as non-Jew is. For those who are unaware, goy literally means "nation." I think it's how people use the word goy that has given it negative connotations.
Interestingly, the frummer I get (or maybe the better people get to know me), the more people use the word goy around me. In the past, I could tell (through body language and word choice) that there was a hesitancy to make general statements about non-Jews to me. Over the last six months or so, this hesitancy is disappearing faster than lottery winnings! I think it tracks their perceptions of me. The more "Jewish" I seem, the less "goy" I seem, and the easier it is to make generalizations or jokes about them with me. Of course, I straddle the line between the two groups, and I probably will for the rest of my life.
I find that I bristle a little while I hear the word goy. It's generally said with little respect, and it is usually followed by a statement about how "other" they are from Jews. (The "other" is a big concept in literature and psychology, but most people know it as the "us v. them" mentality.) I think that using the word "goy" has the effect of dehumanizing non-Jews or otherwise lowering them below Jews. I use the word "non-Jews" simply because I don't have a better one. Of course, "non-Jew" is then defining a person by what they are not and could have the same distancing and dehumanizing qualities! But I think it's less likely to be said by a native English speaker with a sneer. Perhaps because goy is not an English word makes it easier to forget that you're talking about a group of people?
Taking a step back from the words themselves, there seems to be a distinction between who says goy and who says non-Jew or another term. In my experience, those who say non-Jew or a similar term tend to be baal teshuva or a convert (though I do not suggest that BTs and converts as groups tend to use those words; I'm arguing the converse of that connection). There are some FFBs who say non-Jew, but they tend to fall into two camps: (1) those who purposely try to be politically correct OR (2) those who have significant relationships with non-Jews, particularly within their families. As in my case, when someone makes a totally uninformed or disrespectful comment about "the goyim," (plural for goy) I know that they are speaking about my family, my friends, my teachers, and generally a large majority of the people in my life. That's a very different subconscious and emotional reaction than if someone made a similar statement to me about farmers in Micronesia.
My conclusion: I think that people who avoid using the term goy are more likely to be the people with continuing, meaningful relationships with non-Jews, which would support my argument above that we feel the dehumanizing/otherness connotations in the word goy. Quite frankly, I start preparing myself for a bad conversation as soon as I hear someone say the word goy.
Observations, opinions, thoughts?
NOTE: Before "going to press," a friend pointed out that the other word I was trying to think of is "gentile." I'm not sure which camp gentile belongs to in the goy v. non-Jew debate. Personally, I've been known to use it occasionally, but I think of it as an archaic word. The same friend suggested that gentile may be used primarily by people who want to say goy, but think it would be offensive: an apropos analogy would be people who say "people of color." I'm not sure how that word choice translates to "Jews of color," but that phrase seems to have become an acceptable one in the Jewish community and certainly adopted by many (if not most) of the prominent Jews of color that I have read/heard speak.