Great question, and lots of great answers so far.
To me, the concept of a “deal breaker” is something that is absolute and can’t be mitigated by circumstances, so my list is pretty short, and not something I’m proud of. I think in terms of relationships, I really cannot imagine having a genuine, honest, mutually respectful relationship with someone who had a strong belief in god, or someone who wasn’t able to be a good intellectual partner—education is irrelevant, but I would want him to be able to construct a good enough argument to really engage me in discussions, and to understand complex ideas that I find interesting and want to discuss. I’m kind of embarrassed to place such an emphasis on it, but I don’t think it would work otherwise.
And I think cheating goes without saying.
As friendship goes, the only time I can remember intentionally severing a friendship in recent memory was with someone who constantly needed in-depth emotional support and gave nothing in return, even gratitude for my efforts to be there when she (constantly) needed me.