Since I have been reading lots of Classic and more recent YA/children's books I thought that I would pick books using that as a theme ...
1) Anne and Diane in Anne of Green Gables. Though in this case I suppose that Anne wouldn't call it friendship - she would call it a meeting of kindred spirits. This sets a rather high bar for friendship.
2) Judy (Jerusha) and Sally in Daddy-Long-Legs by Jean Webster. Jean would call Sally her best friend, but this would be another example of kindred spirits.
3) Now I have a couple about discovering a friendship with your brother or sister - first I just finished in Emilie and the Sky World by Martha Wells Emilie starts to reconnect with her brother. Note - you can't read this book without reading Emilie and the Hollow World first!
4) Which made me think of From the Mixed-Up Files of Mrs. Basil E. Frankweiler by E. L. Konigsburg which also features a brother and sister learning about each other and becoming friends.
5) The friendship between Danny and Wendell is at the core of all of the Dragonbreath books by Ursula Vernon. They are pretty much inseparable.
6) One of the things that I really liked about Etiquette & Espionage by Gail Carriger is that there are several friendships.
7) How about a friendship that isn't quite what it appears to be ? In Anya's Ghost by Vera Brosgol, a ghost becomes Anya's best friend, but it isn't clear that that is a good idea.
8) In Zita the Spacegirl: Far from Home by Ben Hatke, it is Zita's ability to make friends that enables her to have her adventures and it was because she was picking on her friend Joseph that they got into trouble in the first place.
9) Oh - that reminds me of Giants Beware written by Jorge Aguirre and illustrated by Rafael Rosad. This is a wonderful graphic novel that features a girl, her younger brother and her best friend going on an adventure - testing the limits of friendship and what it is fair to expect of your friends.
10) Friendship and the associated costs are at the heart of The Tattooed Potato and Other Clues by Ellen Raskin. The name sounds very frivious, but this is actually a pretty deep book.
10.5) I also have to give a shout-out to Frog and Toad are Friends books by Arnold Lobel. Classic explorations of friendship and one of my daughter's favorite books when she was younger.