Tentatively, all the things that I can think of wanting in a friend fall into three categories. You're looking for someone enjoyable, someone you can respect, and someone who you find emotionally compatible. . . or, rather than "emotionally compatible," it might be better to say, we look for someone who wants to fill a particular role for us. We're looking for someone to comfortably share in a particular set of activities, who we can exchange some particular kinds of enjoyment with.
Enjoyable people are often entertaining, intellectually stimulating, funny, and kind. Often they are playful and observant. Respectable people, for me, are the people who examine what they believe closely and then live it with passion and competence.
I am particularly interested in anyone's thoughts about what they look for, appreciate, want, don't want, etc. in friends.