Some generalized (very generalized) breakdown of stereotypically preferred cognitive functions by types:
INTJs: See the world with Ni (subjective data), assimilate what they see with Te (objective decision making based on data), and may express their emotions via Fi (subjective decisions based on personal values) or Te (objective decision based on subjective data)
This means you perceive the world and gather data which is internalized and made "permanent" as evidence, then objectively handle that data to accurately make predictions or decisions. It also means expressing yourself may be a weakness, as you will often use your objective decision making tendencies over expressing yourself through your internal value system.
ENFPs: See the world with Ne (objective data), assimilate what they see with Fi (subjective decisions based on personal values) or if prompted their Te (objective process), and may express their emotions via Fi (primarily).
The strongest points of connection would be strong use of Fi and Te, and the differing perception (Ne vs Ni) may provide for interesting conversations and perspective on situations. The INTJ should try to relate to the ENFP (especially in times of stress) using his/her internal values, not objective logic, and the ENFP should strive to respect the INTJ's logical processing tendencies.
There are way better comments and breakdowns on this subject than I just provided. For whatever reason, I was randomly motivated to reply though. You should check out Socionics for more relation-oriented type information (socionics.com). Good luck!
Each of my major relationships has been better than the last thankfully. I had a wonderful time with an INFJ until she lied to me among other things. Next, I was with an ENFJ, but I couldn't handle all the affection she showered me with, especially in public. Then, I was with an ENTP, which only lasted a month and she ended things by coming out of the closet. Most recently, I was with a fellow INTJ, which I enjoyed infinitely more than any of those previous. That also only lasted a month, but this time it was because we live an hour and a half apart and we both work, so she thought it would be best to wait until school resumed. I can't wait!
I dated a ESFP for a couple of months. We both gave the relationship a lot of effort but it didn't work out at all. I just couldn't understand her and she couldn't understand me, hard did we try. So that's probably not a good compatibility.
I find myself attracted to INTJ's INTP's ENFP's and ESFP's (only if they can respect how different we are). Really I say go for the individual not the type, because an unhealthy INTJ is less attractive than a healthy ESFP.
I generally hit it off well with ISTJ and ENFP in general. ESFP too! I really enjoy ESFP confidantes because they do what I want them to do - just listen, and often don't nit-pick my intuition which sometimes is the cause of my own worries/distress.
When I run in to male ENTP or ENTJ I have to be careful, those ones always make romantic sparks.
This is just from my personal experience, it can be different for any INTJ.
I know for sure introverted ENTPs. INTJs are meant to be rare but you always find me - its funny, constantly the tactic has been:
See me from afar, stake out parameter, do a few recognisance missions but don't let on, one you have me hooked on conversation wait until I least expect it and drop a bomb shell - then RUN and hide! ... inevitably I then I come looking for you like the conversation addict I am... :tongue: