I can't think of any. Probably because I'm not used to thinking about them that way - I'm thinking about how to use them. Also, I've learned about how cuisines other than the ones I grew up with use them differently from how people around me did when I was growing up. For example, I might say black pepper and cinnamon don't go together, but they're great in Chinese Five-Spice Powder.
I think it's more a matter of personal preference than any absolute rules.
I agree with GG. I was thinking that maybe you don't want cinnamon and garlic together, but if there is five spice powder and garlic in a dish, then you have both. I have had that and it was good. The other example that came to mind was chilies and vanilla, but chilies added to chocolate that has vanilla is delicious.
I can't really think of any incompatible spices, either. I just recently made an Indian spice mix with 18 different spices/herbs in it! I am one that doesn't like the taste of raw cinnamon in most savory dishes I taste it it, but where it's toasted, and understated, and in things like that 5 spice powder and those countless Indian spice mixes, it is an essential element of the flavor.
I can think of any off the top of my head, but there have been times ive been cooking and questioned the recipe , as it just didn't make sense at the time, cause I probably never tried it before.
I remember the first time I tried a savory dish with cinnamon. I wasnt really into cooking a the time , but loved to eat. My first reaction (before tasting it) was that I wasn't going to like it. I was at a friends house and his wife cooked it, so I knew I had to eat it. After trying it, I was amazed how well all the flavors worked together ( there was definitely garlic, ginger, cinnamon , black pepper) and probably other herbs and spices as well. I have been making something similar ever since.
A friend of mine says he puts sage in is Tomato sauce. I just dont get it, but who am I to question it.
Many times my herbs and spices are kinda grouped together depending on the cuisine im cooking, But I welcome new ingredients and combinations. Not all are home runs , but I always consider it a win when I find or experience a new combination.
Larry, you mentioned grouping spices. I have a separate section for spices that I mentally call "cookie spices": cinnamon, nutmeg, cloves, allspice, mace, cardamom, dry ginger, and vanilla. The only one of those that almost never gets used in savoury dishes by me is dry ginger. For savoury, I use fresh or frozen ginger. And there are certainly other spices that get used with sweet dishes, e.g., black pepper, anise, chilies, and I'm sure there are others I'm not remembering at the moment.