Supporting characters (SCs) have a range of roles to fill in a novel. They can be the loyal best friend, the comic relief, the wise mentor. I'm sure we all have a favorite SC 'type' that we hope to find in the books we read, and recreate in the books we write.
Like MCs supporting characters must display that essential quality trademarked by the Transformers: they must be 'more than meets the eye.'
A pet peeve of mine in books are those narrative that offer intriguing, dynamic MCs (and possibly villains - they'll have their day tomorrow), but SCs who only serve as foils, fillers, and mechanisms by which to move the plot or just serve as another mirror through which to better understand aforementioned MCs.
The best books have SCs in whose lives, hopes, and dreams you're just as invested as what's happening on the main stage. They should be the opening act of show that leaves you breathless, wondering if they actually might upstage the main act. (Note: I had this experience when I saw Calexico open for The Shins a couple years ago.)
Harry Potter demonstrates the essential roles of well-developed SCs. As much as I love Harry, Ron, and Hermione (and yes I think all three are MCs not, SCs), my favorite characters from the series have supporting roles:
Hagrid. What would Harry Potter be without Hagrid. He's an interesting character who combines characteristics of bumbling comic relief with strong warrior protector, making him lovable and reliable at once.
Remus Lupin. Okay, who didn't see this one coming? Everyone knows I have a soft spot for wolves, and Remus is well, just wonderful. His character is compelling because like, Hagrid's, he has a mixture of traits. On the one hand he is a benevolent, witty mentor, but on the other his dark secret makes him edgy and dangerous.
Arthur and Molly Weasley. The parents that Harry never had; quirky, lovable and demonstrative of class conflict in the wizarding world. Mr. and Mrs. Weasley have their own problems to deal with (and we care about those problems) as much as they help with shepherding Harry through his perilous world.
While I've mentioned just a few of my favorites above, J.K. Rowling created an astounding number of SCs who populate Harry's world in substantial ways (I purposely didn't write about Fred and George above because I wouldn't have been able to stop they do so much for the books!) and I firmly believe it's the power of this amazing cast of characters that kept the series lively and enormously successful for its run (and beyond).
As you weave your tale don't forget the fine details of SC creation. Your SCs won't help you or your readers if they're cardboard cutouts. Give them breath and being, give them their due - and believe me, they'll give back.