That's an extremely hard question to answer.
Having experiences in common helps. Sharing the same values. And sharing the same objectives. Many people become friends because they have been pulled together by circumstances because they have the same set of values and objectives. People taking the same classes in university, people working for the same company, people who join a band, the "band of brothers" in the military, etc. People bond when they share meaningful experiences together. A casual conversation probably isn't going to provide enough charge because it's not a very intense experience. Then again, those same intense situations are where people make enemies, too -- they clash over values and objectives.
Notice that if you are primarily self-concerned ... well, it's very unlikely that anyone but yourself is going to have much interest in your life. If all you care about is entertaining yourself, or complaining about your problems, or even getting better, there's not much for people to bond over. (Though it also explains why people like people who appear to take an interest in them.) You need to be interested in something bigger than yourself.
This ties in with stuff I've said before: people won't spend time with you if you're not making their life better somehow. People want to feel excited and alive. If you don't make someone's life better when you're around, they won't come around. People like and respect each other when they share values because it's validating. But I think people bond over shared objectives -- because they need each other to achieve their goals and achieving those goals is what makes them feel excited and alive. A couple is going to be much stronger, for example, if they're both Christian and they both want kids (values + objectives). Fiction is filled with characters who become strong friends because they need each other to survive. A shared objective and shared meaningful experiences might be the only things they have in common.
This is what creates curiosity in many people, I think: discovering that someone else wants the same things that you want, but that neither of you can achieve on your own. You have these (possibly secret) ambitions (however abstract) and you meet someone who seems to want the same things. That creates possibilities; and because it is important to you, it fills you with a kind of excitement. A person like that has something to offer you, because they make your own goals seem more attainable. (Whereas if you both want the same thing and only one of you can have it, it makes you rivals.)
Anyway, this is all thinking aloud stuff. I don't really understand it myself, and I'm aware that there are about, oh, a billion exceptions.
I am very interested in people in an academic or clinical sense. I like to find out as much as I can about people because I like to try to figure out how they work. I also like to help people who are in need, if I can. But that's very different from wanting to be friends with someone.
The only thing better than money is more money.