The #1 breed I will never own is the Border Collie. This is not to say I don't adore RD's Dakota, but the breed is simply not one that I could tolerate on a daily basis. First, I don't like "slinky" dogs. Most BCs I've seen (and there are a lot here in central IA) slink everywhere - if my dog comes into a room, I want people to notice. Second, I can't stand obsessive staring... some call it "the eye", I call it "unnerving". Third, I am completely against what many of the breed clubs are doing to the breed - illegitimize ALL performance titles if a BC is good enough to earn a conformation championship as well? Puh-leeze, I thought versatility was a good thing.
Some other breeds I could not see myslef owning are Labs (bad experiences with them, and they're too soft for me), many toy dogs (but not all - I, for one, love Papillons and Havanese, and most of the giant breeds (especially Danes).
Basically... if it can't keep up with my Dobes, it probably won't be a good fit for my household.