I hesitate to say absolutely no to any breed because if the right individual came along then I would consider it. I'm honestly not much interested by breeds outside the herders, papillons, some guardian types, some sighthounds, and a few of the lesser known sporting breeds (kooikers, tollers, etc).
In general though I wouldn't want a dog that:
-Drools a lot is #1, the more I'm around big jowly breeds, the more I get grossed out by it. I was slimed by a boxer across the leg and it made me feel squeamish. A pyr put a big string of drool on mia's head the other day and I about died. I am really a wimp when it comes to drool.
- Needs professional grooming or has a curly coat. I don't like the feel of curly dog hair and I am far too lazy to actually get them clipped.
- extreme brachycephalic breeds- health issues, activity issues
- dogs with wrinkles- wrinkle cleaning is just not something I want to do
-scenthounds- I really like them but we're on different pages I think.
- most spitz- just don't care much for the look and temperament. I like the herding spitz though (Icelandics, lapphunds, etc)
- most terriers- grooming, temperament. Exceptions would be a well bred jack, staffy, or border terrier.
- I'm not keen on a dog too big to pick up in an emergency though I do love some of the large guardians. I'm just not sure I'd ever own one. Life span of the giant breeds is also something I wouldn't deal with.
- While I feel like I could deal with dog reactivity, dog selective dogs, and same sex aggression, flat out DA is something I'd like to avoid. Unfortunately many breeds I like are DA to some extent.
As for breeds: Neos, huskies, boxers, shih tzu, weimaraner, mini schnauzer, and pekignese round out the list of least likely to own. Neapolitan mastiffs are definitely #1 least likely to own. I met my first ones this summer and all I could think of was drool and wrinkles. When it got to moving, drool flew all over it, wrinkles were just flying everywhere.... just about the opposite of what I like in dogs.
The only toy breeds I'm interested in are papillons, cavaliers, and cresties. I might consider a crestie or a cav but I really think I'll probably just stick with paps for the little dogs in my life.