INTP, close enough to INTJ...
I rarely cry. Maybe twice a year, on a bad year.
Exceptions include things like particularly good movies, TV shows, books, games (though this is particularly rare), *insert storytelling medium here*. I can occasionally cry to these things. I view them as an opportunity to indulge in my emotions, so I let down many of my conscious guards against emotion, but even then, it takes something really good to get an emotional reaction from me.
As for a more general view, not necessarily crying, it's still really rare. I don't think I just 'break', more that it gradually builds up and effects me more and more.
One thing I'm curious about, though. I find that when I can't deal with emotions, it's because I am unable to express them (inferior Fe, at least according to MBTI...). I have severe reservations against showing emotions (I do show minor things, like laughter, happiness in small doses, frustration, etc. But big things, like love or sadness are out of the question), and it's very hard to let down these barriers. Exceptions are like I explained above, which I usually do in private, and if anyone saw me, it's "ok", because you're "supposed" to feel emotional to those things. (Oh right, my question...) Basically, how do INTJs react, how does tertiary Fi affect them (and inferior Fi for ENTJs)? Maybe, the 'breaks' happen because you don't even realize you're having an emotional reaction to something, and it just builds up until you explode?