Been thinking about this a bit, lately, actually. Because I've made very few friends up here, and I'm having problems accepting the advances of a couple people who are trying to become my friends. Hmmm. More later, when I'm coherent and not stuffed with gumbo. :)

This is all very subjective, but I'll give you my 2 1/2 cents.

what makes you want to be friends with someone? A no-nonsense attitude. Acceptance. A willingness to share little pieces of themselves.

what makes you want to go out of your way to get to know someone? The above, along with the feeling that my life would truly be better with them in it.

is there anything that'll make you not want to be friends with someone? Telling me I'm wrong all the time. Having a closed mind. Making me do all the reaching out, then ignoring my outstretched hand.

why do we have friends, period, and what do we gain from the experience? Humans need companionship. It's an instinct thing. We need it or we go nuts. What do we gain? A challenge to grow and to better ourselves. A different perspective on life from someone we trust. The warm fuzzies that come from spending time with our friends. Comfort when someone stays by our side during a hard time. The rare moments when the masks completely fall away and we truly know we have someone who accepts us.

I wish you'd had more replies to this because I set it aside to come back and read later. =) I don't have much in the way of an answer, myself... I want to be friends with people that meet two criteria; 1. we have a good time together and 2. our relationship is mutually beneficial.
There're different degrees of friendship, too. Some people who I just really admire and feel a connection with but don't really interact with very much, I still call friends. People who know they can call me if they need something even if I haven't seen that person socially in four years... that's a friend too.

I don't make friends with people who blatantly disrespect me, have damaged people I care for, or myself, or who I know ahead of time I can't respect.

Why do we have any relationship? There is comfort and strength in numbers.

So much of my 'why' is intangible -- the people I seek out friendships with are people I feel a sense of connection to, and why that connection happens is something I don't know. But there are reasons I don't pursue friendships; if I'm going to be close to someone I want/need them to have a high level of self-awareness or at least they need to try to have a high level of self-awareness. They need to care about something of the same things I do, either for those things themselves or because I care about them. I won't be friends with people who are abusive (either overtly or un-overtly) or who can't discuss things rationally or who won't respect my boundaries -- I might be friendly to people like that in passing, but I won't develop a friendship with them.