Here are suggestions for books that pick up on the sword and sorcery, quest, and dragon aspects of "Eragon":
The Dark Tower series by Stephen King
The final hour of Roland Deschain's quest for the Dark Tower has arrived. This tower has been his Holy Grail, the quest his raison d'etre-- and Roland will not stop until he reaches the magical and dangerous tower that stands at the nexus of all time and space.
The Sword of Shannara by Terry Brooks
"An epic fantasy of gnomes, trolls, dwarfs and elves in which a simple man, Shea Ohmsford, is pitted against the greatest power of evil the world has ever known."-catalog summary
The Iron Dragon's Daughter by Michael Swanwick
"...the heartrending story of a changeling child who is kidnapped to a realm of malls and machines and enslaved in a vast, infernal factory.
Ultimately she escapes and attempts to educate herself about this alien world, while being tormented by visions of the life she was denied."-catalog summary
The Dragon and the George by Gordon R. Dickson
"Through no fault of his own, the once human Jim Eckert had become a dragon. Unfortunately, his beloved Angie had remained human. But in this magical land anything could happen. To make matter worse, Angie had been taken prisoner by an evil dragon and was held captive in the impenetrable Loathly Tower. So in this land where humans were edible and beasts were magical--where spells worked and logic didn't--Jim Eckert had a big, strange problem."-book jacket summary
The Last Dragonlord by Joanne Bertin
"Linden Rathan is the last of a race of weredragons--magical, nearly immortal half-humans who can transform themselves into mighty dragons.
Linden is one of three dragonlord judges who will determine the next ruler of a true human kingdom. Political and sorcerous machinations and ancient hatred threaten the dragonlords' decision, and Linden must sort out the good from the evil, all the while fighting loneliness and despair. When he meets a beautiful young sea captain, Linden thinks he might have a chance at love after all."-Amazon.com summary
Dragon's Winter by Elizabeth Lynn
"...twin boys are born to the dragon king of Ippa, though only one-Karadur Atani-is born of dragon blood. But Karadur Atani will never become a dragon, for his bitter twin brother steals his talisman and leaves him trapped in the body of an ordinary man. As a powerful wizard rains death and destruction on the people of Ippa, Karadur Atani leads his warriors into war-to challenge his wizard brother and to reclaim his destiny."-catalog summary
The Book of Knights by Yves Meynard
"Spurred on by a miraculous book depicting the deeds of famous knights, a young boy leaves his foster home to seek his own destiny as a hero.
The first English-language publication by French Canadian author Meynard evokes a fairy tale-like atmosphere in his depiction of the trials and tribulations of his young protagonist. The author's lyrical style accentuates the allegorical nature of this intensely compact tale of self-discovery."--Library Journal summary
Blue Sword by Robin McKinley
"Harry, bored with her sheltered life in the remote orange-growing colony of Daria, discovers magic in herself when she is kidnapped by a native king with mysterious powers."-catalog summary
Birth of the Firebringer by Meredith Ann Pierce
"Jan, the prince of the unicorns, is high-spirited, reckless-and the despair of his mighty father, Korr. Reluctantly, Korr allows Jan to accompany the other initiate warriors on a pilgrimage. Soon Jan's curiosity leads him, along with his friend Dagg, and their mentor, the female warrior Tek, into the greatest dangers-deadly gryphons, sly pans, wyverns, pards, and renegade unicorns. Yet time after time they are rescued, leading Jan to wonder: Am I the heir to a special destiny?"-book jacket summary
Mary M. Buck