I actually did a My Favorite Things Post on this a couple of years ago. Those names are still valid so I'm keeping them on the list (yay for copy and paste!), but there are certainly more I can add.
A friend, family member, teacher, enemy, however they may be connected to the main character there are some supporting characters that capture my attention (and love) just as much. Some authors (Megan Whalen Turner) are crazy good at making the most minor characters seem fascinating with just a few sentences. Sometimes, it just depends on who I connect with in a book. I find myself wanting more of their story, to know what makes them tick. In some cases I desperately want the author to get to work already, and deliver a novel about that character. In some cases, I like being left with the devices of my own imagination. Either way there some secondary characters that have completely captured my devotion.
Chaz Santangelo (Jellicoe Road by Melina Marchetta)
I just love him. I'm going to admit it: I love him more than Jonah Griggs. I liked him a lot the first time, but the second time through I fell hard. I think he is awesome and he intrigues me. Marchetta could have made him a mere plot pusher, the one who reveals certain truths to Taylor, but she gave him a fully realized personality and some amazing lines.
Rob (Rebel (UK)/ Wayfarer (US) by R.J. Anderson)
Rob has many characteristics I like in male characters so it is not really surprising that I find him so fascinating. There are several mysterious incidents in his past mentioned (one major very dark one in particular) that really make me want to know his entire story and how he came to where he now is.
Bunter (Strong Poison, et al. by Dorothy Sayers)
I admit through most of the Lord Peter books I saw Bunter as just a very loyal servant and helper to the awesomeness that is Peter. But then I read Strong Poison, where Peter makes allusions to Bunter's behavior off the job, and Bunter manages charm all sorts of information out of serving women. I suddenly wanted him to have more page time. And books of his own.
Arachne (The Drowned Vault by N.D. Wilson)
This is the Arachne from mythology complete with spiders. As much as I hate the spiders, I love her and what Wilson has done with her character. I want her backstory (other than what we know from the myth) something fierce. Her relationship with Gilgamesh in this book intrigues me greatly. She seems way too good for him on any level, and yet there is definitely some history there I would like explored more.
Sophie (Jinx by Sage Blackwood)
The hints of history we get in Jinx of the drama that is Sophie and Simon can have no other effect than to make you want to know more about both of them, but for me I found her to be the particularly intriguing one. It is exciting that there will be more of her in the sequel, but I would really love an adult series of these books all about Sophie and Simon.
Inspector Wolf (The Inquisitor's Apprentice by Chris Moriarty)
And speaking of characters from MG books I would love to have an adult series about, Inspector Wolf is actually number one on that list. He works so well as the mysterious mentor of Sacha and Lily, but man what I wouldn't give to have his whole story and things from his point of view.
Red (The Bitter Kingdom by Rae Carson)
On the flip side, here is a child character in a YA novel I think is deserving of her own book. Or series. I love this girl and I think it would be fascinating to read about her life following the events in The Bitter Kingdom.
Marianne Pinhoe (The Pinhoe Egg by Diana Wynne Jones)
Okay, I suppose technically Marianne is not a secondary character as her name appears in the title for this book. BUT, she is newly introduced in this, the last volume of the series, and definitely works as a foil for Cat, who is after all training to be the next Chrestomanci. Then there is the presence of Christopher, who just overshadows everyone else no matter what (and rightfully so). I want to know more about Marianne. I want to see her grow, learn alongside Cat, train with Christopher. In many ways, she served a similar function in this book to Cat that Millie does to Christopher, but relative to their own personalities. And man do I wish we could see that play out. *sobs because this will never happen*
And then there are all the character from Megan Whalen Turner's books...
The Magus (what is his name), the MOW, Agape (who has to be developing a serious complex by now), Lady Heiro, Philologos (he is my favorite attendant), Ion (both of them), and I could go on and on...I told you MWT is good at this.
Of course the list wouldn't be complete without all the amazing Harry Potter characters either. Every single character in these books leaves an impression.
How about you? Who are some of the secondary characters to capture your heart and imagination?