This is what I've got so far. I'm missing 3,10, & 12 and it's driving me crazy. The dragon ones are so familiar. I will dig out more of my books in boxes and make a trip to the library. If I get them I will send in a revised list.

1 Dragonbone Chair by Tad Williams
2 Game of Thrones by George R. R. Martin
4 Assassin's Apprentice by Robin Hobb
5 Goblin Quest by Jim Hines
6 Spirit Gate by Kate Elliott
7 Harry Potter & the Sorcerer's Stone by J. K. Rowling
8 The Golden Key by Melanie Rawn et al.
9 Furies of Calderon by Jim Butcher
11 Magic of Recluce by L. E. Modesitt, Jr
13 The Redemption of Althalus by David & Leigh Eddings
14 Lies of Locke Lamora by Scott Lynch
15 His Majesty's Dragon by Naomi Novik
16 Skewed Throne by Joshua Palmatier
17 Ship of Magic by Robin Hobb
18 Eye of the World by Robert Jordan
19 Tigana by Guy Gavriel Kay
20 Name of the Wind by Patrick Rothfuss