Besides titles listed below, I have some kind of a copy of every gold medalist, in all cases possible a nice hardcover copy, and generally copies of the whole series when the medalist was one of a series. I am noting cases where I know I don't and beyond this list I will just have to check.
The Voyages of Doctor Dolittle by Hugh Lofting, 1923, I have, and several other titles, but not the entire series.
Caddie Woodlawn, by Carol Ryrie Brink, 1936. My hardcover is a very beat-up ex-library with no dust jacket. I also have the sequel, Magical Melons, an older ex-library, again with no dust jacket. Both wonderful and highly recommended for anyone who enjoyed the Little House series.
Roller Skates, by Ruth Sawyer, 1937. Both my copy of this and of its sequel, published both as The Year of Jubilo and Lucinda's Year of Jubilo, are paperbacks.
The High King, by Lloyd Alexander, 1969, is part of a five-book series. I know I have some and not others. Will have to check which.
Julie of the Wolves, by Jean Craighead George, 1973, is part of a series. I have the Newbery winning title in hardcover but other titles are either in paperback or I don't have at all. Again would have to check.
The Grey King, by Susan Cooper, 1976, I have no hardcover copy of the second book in the series (or the first if you count Over Sea, Under Stone as a prequel), The Dark is Rising.
Roll of Thunder, Hear My Cry, by Mildred D. Taylor, 1977, is part of a series. I have maybe one of the other titles in paperback and one in hardcover.
Dicey's Song, by Cynthia Voigt, 1983, is part of a series. I have some of the books but not all.
Sarah, Plain and Tall, by Patricia MacLachlan, 1986, is part of a trilogy. I have no print copies of Skylark or Caleb's Story.
Shiloh, by Phyllis Reynolds Naylor, 1992, is part of a trilogy. I have no print copies of Saving Shiloh or Shiloh Season, and my copy of Shiloh leaves something to be desired. It is a hardcover but not library binding, one of those Weekly Reader types with the art printed on the cover, no dust jacket.
The Giver, by Lois Lowry, 1994, is part of a series. I have none of the other titles.
A Year Down Yonder, by Richard Peck, 2001, is part of a series. Don't think I have a print copy of A Season of Gifts but would have to check.
Crispin: The Cross of Lead, by Avi, 2003, has at least one sequel of which I don't have a print copy. Possibly is or will be a series.
(You didn't hear it from me, but right here is where the gold medalist books stopped being good with some exception for The Higher Power of Lucky.)
Kira-Kira by Cynthia Kadohata, 2005, my copy is hardcover, but not much better than my copy of Shiloh. I actually saw a better copy at a thrift store, but they wanted three bucks for it and Kira-Kira is not worth three bucks.
Criss Cross, by Lynne Rae Perkins, 2006, is one of at least two books, possibly more. I don't have any of the others and thought I was going to die reading this one, but as a completist I guess I should collect the others, but don't promise to read them. Nothing is particularly wrong with the book except that parts are mildly interesting and other parts are horrendously boring. Very true to life but a bit too much so.
Beyond the above titles I would have to check what I need. All but the last twenty years or so are mostly ex-library and the last twenty years or so are mostly not.
2013: The One and Only Ivan by Katherine Applegate (HarperCollins Children's Books)
2014: Flora & Ulysses: The Illuminated Adventures by Kate DiCamillo (Candlewick Press)
2015: The Crossover by Kwame Alexander (Houghton Mifflin Harcourt)
2016: Last Stop on Market Street by Matt de la Peña (G.P. Putnam's Sons/Penguin)
2017: The Girl Who Drank the Moon by Kelly Barnhill (Algonquin Young Readers/Workman)
2018: Hello, Universe by Erin Entrada Kelly (Greenwillow Books, an imprint of HarperCollins Publishers)
I haven't read the 2008-2018 winners, but pretty much have to as forty years ago I made a vow to read every gold medalist and since the award began in 1922 and I've already read this many books I have to read the remainder even if it kills me. Sometime between 1984 and 1988 I caught up and threw a party with cakes decorated to represent each title. In 1998 I caught up completely and had my photograph taken with all the books up to that point. I came across the picture the other day. I should really do an update I guess, but barring miracles it will not happen in 2018.