I've gotten along best with INFPs, ISFJs, ESTJs, INTJs and ISTPs.
INFPs have this off the wall humor and are quite animated, but there's something about them that I just click with. They're like ENFPs but I can handle them since they're much more reserved. We just find this mutual comfort in just being with each other.
ISFJs are basically like me, but are instead geared toward people. They focus their skills toward helping other people. The fact that they're so calm, organized, directed, AND friendly which is what I lack makes me turn into a puddle around them.
ESTJs can go either way. I've had two ESTJs as teachers and they're just so frustrating. I've worked with an ESTJ and it was really fun. We both had the same goals in mind, but worked toward them in slightly different ways. He was able to get the ball rolling on things while I handled intricate details. I liked the partnership aspect because of how we complimented each other.
INTJs are really just intense geeks. I've learned to appreciate the N side of things without the help of MBTI, so I can blend in with INTJs easily. They're still so distant.
ISTPs are cool people. They have the same reality based outlook and the ability to understand how things work from a manual labor point of view. I really admire their technical skills. They can figure technical things that involve using their hands easily which is just awesome.
The types I have a problem with....
ENFPs and ESFPs come to mind first. They're all over the place. They're random. They connect everything to Fi which makes me feel slowed down so much. However, they're really great to help you see the lighter side of life.
ESFJs, oh God. They're like walking charm school teachers. They're always on my back about how I act toward people. I regulate my actions on my own, I don't need them telling me what's right or wrong. They show me that just because someone is able to be organized and purposeful doesn't automatically make them interesting people.
INFJs, I haven't encountered many of them. I know one that I talk to on a regular basis and I think the world of her. She has the same tendencies toward me though that other INFJs have had. They tell me to stop contemplating and being so serious and go do something worthwhile.
As for temperaments, it depends on the person. NT is the first one that comes to mind that I can click with right off the bat. However, the only thing that gets in the way is when I can't think quickly enough for them and they get bored of me. I find NTs the most intriguing out of the four temperaments. Next would be SJ, then SP, then NF. SJ's tendency to have it together gets me in. SP's, though, they always look at me with this look of, "Why are you so fucking serious?" NFs I just have to take in small doses because I don't have the energy to deal with the idealistness all the time.