I'm an ENTP male and my best partners-in-crime are ENFP, INTP and xNFJ.
My absolute favourite Partner-In-Crime at the moment is a male ENFx friend. We immediately think the same thing at the same time and come to similar conclusions, but look at things differently and tend to have interesting views and perspectives that the other can learn from.
If we're talking about romance, My attraction to ENxx tends to be more "public" and "social"; like wanting to ride a wild horse or a sports car. I wouldn't say "conquer" because I enjoy the company of other wild spirits and wouldn't want to "tame" them. I guess this fits your description of "partner-in-crime" better?
My attraction to INxx types is a lot more subdued and personal. I love how INFx women can sometimes kick my butt with the simplest and most elegant reasoning. I also find that INTP women can be wonderfully kinky, INTJ women have brains that are extremely pleasurable to explore. The few women in my life that I can imagine marrying are almost all INFx.