[mild spoilers ahead]
Amber's distrust of heroism - and the collateral damage it causes - places Zelazny (like contemporaries such as Donaldson, Harrison and Moorcock) in dialogue with the newly-minted tropes of the genre after the Tolkien boom.
It being Zelazny - it's also at least superficially about a load of superhuman magnificent b**tards having a right old barney (see also Lord Of Light and This Immortal).
The scoundrels in question are the fourteen princes and princesses of Amber's royal family, squabbling for the vacant throne while also defending the kingdom - the literal centre of the multiverse - from external nemesis. Long-lived heirs to ancient powers, they are able to walk between worlds, discerning possibilities and picking the best (or worst) reality has to offer.
Our narrator is missing-presumed-dead Prince Corwin, who starts the first of the four books (all practically novella-length) collected here as an amnesiac exile on our Earth. Over the course of the Chronicles, he regains his memory and takes a lot of bad decisions which usually involve trusting his relatives.
Notwithstanding this drama, Corwin ultimately helps to save the day from the forces of Chaos* threatening to unpick the warp and woof of Amber (and thus the universe). He also becomes less of a self-obsessed ass, which by the standards of his family is no small achievement.
A big part of the pay-off in reading the Chronicles is the gradual revelation that he's not the chosen one, that he doesn't want the throne, and that someone else in the family has been on an even longer emotional journey than he has - that is to say, they are the protagonist.
This reversal of expectations, this sense of displacement from cliche is pretty fundamental to Amber's appeal. Take our apparent heroes for another example.
All of the Amber siblings are capable of heroic acts, but they are monsters too. They win the day not necessarily because they are better than their opponents - on that, your mileage will vary - but because they are more resourceful and more ruthless. Entire armies are recruited from across the planes and perish in their service, while the series is ridden with their one-on-one fratricidal cruelties and plots.
They are Olympian in every sense of the word. And now that I come to think of it, the whole family drama lays itself wide open to a Freudian reading. Hmmm.
Given the above, it's no surprise then that altogether the best scenes in the books, as is usual for Zelazny, are dialogue. It's a delight to read passages with the squabbling sibs aiming rhetorical barbs at each other, like characters from a multi-planar telenovella.
Elsewhere the writing can be described - like much 70's SFF - as pulp with a side-order of experimentation, usually taking the form of fragmented slide-show descriptions of travel between the worlds. For my money, this side of the Chronicles hasn't aged as well as it might, although I suppose its jarring quality heightens the sense of displacement, this time from the text itself.
And Amber's age does show in its portrayal of women as lovers, wives and femme fatales, but at least tends more toward sins of omission rather than Greg Mitchell style commission.
But in its confounding of expectations and in the richness of its dysfunctional family, Amber is greater than the sum of its parts. It might not be Zelazny's masterpiece - that's still Lord of Light - but in its ambivalence and ambiguity lies its lasting value.