I'll admit upfront that I've never been a big fan of Roger Zelazny's "Chronicles of Amber." I've read the series -- at least the part of it published in the 1970s -- and found it intellectually interesting, but something about its characters and plots just didn't click with me. That's certainly no crime; lots of very good books aren't to my taste. The only reason it bugs me in this particular case is because Gary Gygax included the series in Appendix N as an influence on AD&D. Likewise, I enjoyed Jack of Shadows, also by Zelazny, which shares similar themes with the "Amber" books, thus making my own lack of enthusiasm all the more peculiar.
The series kicks off with 1970's Nine Princes in Amber, which is the one book of the original five I enjoyed without qualification. The book begins with a man named Carl Corey who finds himself in a secluded medical clinic, unable to remember who he is or how he got there. In time, he learns that he was the victim of an automobile accident and that he was sent to the clinic at the expense of his sister. This information convinces Carl to escape the clinic and seek out his sister, hoping it might shed further light on his situation.
When he finds his sister, she addresses him by another name -- Corwin -- and his reluctant to let him stay with her. She does, however, which enables Carl/Corwin to come across a strange set of Tarot-like cards, through which he sees people and images associated with his life, a life he still cannot remember. In addition, he's contacted by a brother, Random, who asks Carl/Corwin for his protection and in turn offers to take him back to a place called Amber. Since Carl/Corwin has no idea what is going on or why, he agrees and soon finds himself in a strange reality, where he and his family (including eight brothers, of which Random is only one) wield remarkable powers and are forever plotting against one another for control.
Nine Princes in Amber has a lot going for it, chiefly the mystery of Carl Corey's identity and its connection to what he perceives to be happening to him. It also includes some fascinating speculations regarding alternate realities and Chaos, themes that recur not just in Zelazny's other works, like the aforementioned Jack of Shadows, but in a lot of late 60s/early 70s fantasy. In retrospect, it's this that I think appealed to me most way back when and it's this that still appeals to me even now. The style of fantasy the "Amber" series represents is one that seems largely to have fallen into disfavor as the 1970s wore on and the influence Tolkien -- and his pastichists like Terry Brooks -- became ever greater. Although Gygax's published writings betray comparatively little influence by authors like Zelazny, he continued to express admiration for their writings and several of his unpublished projects, such as Shadowland, might have taken D&D in a more Zelaznian direction.
I personally see the influence of Zelazny over Tom Moldvay's classic Castle Amber, perhaps unsurprisingly. As a younger person, I was confused by the title of this module, which recalled Nine Princes in Amber, despite having nothing to do with the novel overtly. Yet, its contents, while explicitly tied to the Averoigne stories of Clark Ashton Smith, nevertheless seemed very "Amber"-like to me. The Amber family is filled with a variety of ambitious, Machiavellian personalities and their rightful head, Stephen, has been "murdered" by his family and whose salvation depends on items obtained in an alternate reality. Certainly the connection between Moldvay's work and Zelazny's is not strong, but it's there, I think, and I'm surprised more people don't seem to comment on it.
Regardless, the "Chronicles of Amber" (the first five books anyway; I can't comment on the later ones) are worth the read, if only to mine for ideas. They're definitely quirky in their sensibilities, but that's a positive thing in my estimation. D&D -- and fantasy gaming in general -- could use more quirkiness these days.