I actually tend not to get along with people like me that well. I meet another me, and we both just wait for the other to initiate things. My most successful friendships have been with extroverts (or more social introverts), with a few exceptions.
The one who buggers a fire burns his penis
-anonymous graffiti in the basilica at Pompeii
I made everyone on the leadership team take the MBTI over the summer when we were e-mailing and organizing. She told me later she was fuming mad that she was forced into doing it but didn't want to cause ruffles with someone she hadn't met so she took the test and immediately ignored it.
Why would you *force* someone to take the MBTI? And secondly, why would they listen to you? I don't respond well when people try to force me to do anything.
But to answer the original question, most of my friends...ok, almost ALL of my friends...are either NFs or NTs. There's one exception who is an SJ. I met most of them at college. I have this habit of making friends with the most extroverted people around (usually the "life of the party" person), and then I always meet tons of people through them. Don't really know why, it just keeps happening that way.
As for why they are all Ns, I imagine it's because I'm a very strong INTJ, and other types just have a hard time connecting with me, or me with them. The exception is the ESTJ friend of mine, I think we connect on a T level.
For me playing D&D and other role playing games - the kinds with paper and pencil and dice, not computer - helped me to make friends. I also go to science fiction conventions and gaming conventions. I don't necessarily make friends there but I find it fairly easy to socialize with people in that situation.
Not only do I share hobbies and interests with them, it seems like many people who like role playing games and science fiction are also NTs. So we share both hobbies and personality types.
I also find it helps to make friendships with other people who are eccentric, even if they are not eccentric in the same way you are. There often seems to be an unspoken rule that you accept their quirks and don't poke fun and them and they do the same for you.
The simplest way to find people like you is to systematically determine the unworthiness of all people you encounter of your friendship, then when you find someone worthy engage them in deep conversation as often as possible.
Whenever you find yourself in a group of people you are unfamiliar with, bring up topics that are important to you, if people respond then you will be in your element and far better able to distinguish those you don't want to be friends with from those you do.
Do not mistake shared interests for compatibility.
Some people you meet would make fantastic friends but have very few shared interests with you, to feel them out bring up topics that everyone has some level of a connection with (take your pick from any of the sensitive topics). If you are able to bring up a worthwhile conversation then people will respond and reveal themselves to you.
INTJs should be able to do this quite easily due to their Te, INTPs might have a harder time with it.
I guess as an INTP who's unwilling to direct conversations you'll need to become very aware of the people around you and be able to spot the signs of a potential ally.
I try to be friends with everyone and put more effort into spending time with the people who interest me. It usually works. I'm good at finding similar interests with others- the thing I feared was that I seemed too nerdy to others. On the other hand, I never met an NT or NF who was intolerant of 'nerds'- so it is just like a force-field that makes many Sensors go away.