Hmmmm...I can't think of any specific bag I wouldn't buy because it's common. Maaaaaybe the LV mono bags?? But, really the main reason I haven't bought one is simply because they haven't called to me yet.
If one does, I'll buy it.
I will, however, avoid it bags and it bag style trends because they will tend look dated over time. I'm trying to buy forever bags that don't scream a particular year or era. So, it's not so much that I'm trying to avoid seeing my bag everywhere as it is I'm trying to avoid eventually seeing my bag nowhere - not even on my arm. LOL!
On the other end of the spectrum, I'll also tend to avoid obscure, unpopular bags even if I like them because if I want a change, I want the resale market for my bags to be good.