I'm pretty sure my ideal mate is just a female ENTP with an Icarus Complex like mine.
I've tried every other P type, and there's always been some middling criticism that wouldn't let me commit fully. (I've even tried 4 of the 8 J types!)
Let's see...types I have dated and why it didn't work:
ISTJ - She had way too many arbitrary rules about how EVERYTHING in the relationship should operate. I was initially attracted to her because she was musically talented, but only years after she dumped me (on AIM, 10 minutes after getting home from seeing our favorite band together, btw) did I finally realize she had just Si-memorized purely by rote how to play her instruments, and there wasn't really any depth of creativity there at all.
ESTJ - This was great for all the verbal sparring but eventually her "I have to go to college and trust my life to God" attitude kinda got to me, despite her brilliant wit. It was a shame. (Also seemed to prefer guys who were significantly less intelligent than she for the easy control, so this didn't work out too well with me because we were pretty mentally on par and that's what it made exciting for me.)
ISTP - Umm I lost my virginity to her and sex was really novel on its own at the time. We broke up like a month later because we had pretty much nothing in common.
ESTP - Fun for a brief hookup, no substance.
ISFP - Several dates went reasonably well and we get along ok, but...at the end of the day nothing really in depth to talk about.
ESFP - Fantastic sex and neither of us even made any pretense at it being anything else. She ended up getting a stable boyfriend and I haven't seen her in years, but if she showed up I'd totally be down for it. Aside from that, well...same problem with other SPs--no real depth of conversation in most cases.
INFP - Great relationship based on common Ne
at first, but Fi dominance gradually wears down at me until I just don't really want to talk to them anymore because they see themselves as so open-minded that they'll automatically reject my suggestions that they're closed-minded in certain situations. I guess that's why socionics call this one the "illusory" relationship. I love love love being friends with INFPs but relationships just don't seem to work out long term.
ENFP - Generally pretty good until we get bored with each other and move on to the next toy, I love the Ne dominance and since it's in the driver's seat, I can tolerate the secondary Fi...but I still find myself wishing it was Ti.
ENFJ - Bonded very closely at first over each other's strong charismatic energy, but eventually found that we didn't really have much in common at all, besides a twisted sense of humor/penchant for feigned arrogance. We're still on good terms but don't talk often.
INTP - As close to perfection as I've found; same functions but I just can't get over my tendency to try to mold them into ENTPs. I get tired of talking to Ti and want Ne to come out and play more often. I've dated a couple of INTP women and it's never really quite worked out, just seemed like it should each time. It always feels right at first and then totally collapses in a painful and dramatic way. Not fun.
ENTJ - Some things in common; seemed like a pretty promising relationship at first, but Te/Ti just got in the way too much. She felt like I wasn't proactive enough and I felt like she was too controlling...typical ENTP/ENTJ.
So it looks like the types I have not dated as of yet are: ISFJ, ESFJ, INFJ, INTJ and ENTP.
Somehow I doubt an SFJ would work out very well for me, but ENTP may not be the only option...I could certainly deal with trying out an Ni dom woman, but they're pretty few and far between, in my experience.