This article is from the rec.arts.sf.written FAQ, by Evelyn C. Leeper firstname.lastname@example.org with numerous contributions by others.
There are two answers here, a short one, and a longer one which also
includes opinions on the quality of the books.
From J. Hunter Johnson (email@example.com):
As with other series, the Asimov books can be read in published order or in
chronological order. First-time readers should probably read the books in
published order to avoid some of the spoilers present.
The chronological order of the novels by Asimov or approved by his estate
The Caves of Steel (1954)
The Naked Sun (1957)
The Robots of Dawn (1983)
Robots and Empire (1985)
The Stars, Like Dust (1951)
The Currents of Space (1952)
Pebble in the Sky (1950)
Prelude to Foundation (1988)
Forward the Foundation (1993)
Foundation's Fear (1997, takes place after the first chapter of Forward the
Foundation and Chaos (1998)
Foundation's Triumph (1999, takes place after the first chapter of
Foundation and Empire (1952)
Second Foundation (1953)
Foundation's Edge (1982)
Foundation and Earth (1986)
A full chronology including short stories and unapproved novels can be
found at http://www.clark.net/pub/edseiler/WWW/insane_list.html.
From Richard Harter [note this includes critical comments as well as
a description of the series]:
In his youth Isaac Asimov constructed three distinct major fictional
universes, each thematically separate, the far future Foundation
trilogy, the near future series of short stories about positronic
robots, and an intermediate series about the conflict between Earthers
and Spacers, the latter being potentially in the same universe as his
earlier robot novels.
Much later, after a successful career as an author of non-fiction
expository works on a wide variety of subjects, he wrote a sequel to
the Foundation trilogy, "Foundation's Edge". Not content with this he
embarked on a series of novels to tie his various universes together.
Since his death the composite universe has been extended by authorized
novels by David Brin and Greg Bear.
The time line for Isaac Asimov's composite universe:
(The later works are marked with stars.)
EARLY (IN THE NEAR FUTURE)
The End of Eternity 
The Rest of the Robots
EARTH AND THE SPACERS
The Caves of Steel
The Naked Sun
* Robots of Dawn
* Robots and Empire
The Stars Like Dust 
The Currents of Space
Pebble In The Sky
* Prelude to Foundation
* Forward the Foundation
Foundation & Empire
* Foundation's Edge
* Foundation & Earth
The theme of the original Foundation trilogy (a series of short stories
and novellas packaged in three volumes)is the unfolding of a grand
planned history, the Seldon plan, the threat of the plan being
destroyed, and the plan being saved. The trilogy has its faults. Asimov
was quite young at the time: His appreciation of the variety of human
behaviour was limited and many of the details of his universe were
quite naive in conception. The quality of his prose is subject to
debate. The stories were somewhat dryly intellectual in conception.
None-the-less there is a grandness of conception and intriguing
puzzles. They also have one of his few great characters, the Mule. The
real hero, however, of the trilogy is the Seldon plan itself. The
Foundation stories are a triumph of science fiction as the literature
of the idea as hero.
In his early years he wrote two excellent novels, THE CAVES OF STEEL
and THE NAKED SUN, both sparse. They carried the robots of I, ROBOT
into a future of spacers vs Earth, the spacers having a mixed
human/robot culture spread across many worlds and Earth a city based
culture with a fear of robots. Earth is technologically backwards and
its residents are psychologically restricted to their caves of steel.
(The spacers vs Earth theme is an elaboration of an earlier novella,
Mother Earth.) Both are detective stories in an SF setting. Both rely
on two strong characters, the human detective, Lije Bailey and the
human appearing robot, Daneel. A thesis of the novels is that the
future of humanity lies in a C/Fe culture, i.e., in the equal
partnership of human and robot.
FOUNDATION'S EDGE was written many years later. His early novels was
sparse; FE is the first of a series of bloated novels. In my opinion it
is the first step in his disowning the Foundation trilogy. The entire
basis of the character of the Mule is destroyed. The Seldon plan is
disowned as being ultimately worthless and a cheap-jack psionic
mysticism is offered in its place.
Having returned to the worlds of his youth, Asimov determined to unite
his two grand universes. There are no robots in the Foundation universe
so it was necessary to eliminate them. He did this in two more bloated
novels, THE ROBOTS OF DAWN and EMPIRE AND ROBOTS. In these he disowns
the thesis of the C/Fe culture. The spacers are discounted as not being
viable; Daneel, on the other hand, is promoted into a mind-controlling
demi-god. He followed these two with a third bloated novel, FOUNDATION
and EARTH, a sequel to FOUNDATION'S EDGE in which it is ultimately
revealed that Daneel is the master mind behind human history.
This was, for the nonce, the capstone of his of his campaign to disown
the work of his youth by rewriting the juice out of it. The value of
the Seldon plan had been discounted; the Mule had been emasculated;
Daneel had been destroyed by deification; and the C/Fe thesis had been
discarded. He wasn't done.
PRELUDE TO FOUNDATION and the sequel FORWARD THE FOUNDATION are
set on Trantor; nominally they are about how Hari Seldon brings
about the Seldon plan. Both are farragos of implausible
melodrama. Concealed within them however is the final discounting - the
revelation that the Seldon plan was never feasible in the first place.
 The Bear, Brin, et al novels are a continuation of the melodrama.
In the words of bard, they are full of sound and fury, signifying
 THE END OF ETERNITY is not part of the series but it implicitly
 THE STARS LIKE DUST is an early work; it isn't quite consistent
with his later works but is consistent with the earlier novels. It
features a radioactive Earth whose radioactivity is due to a nuclear
 In SECOND FOUNDATION the original plan was somewhat makeshift, a
"best we can do" at the time job. The one sour note is the idea
advanced in SECOND FOUNDATION that the Second Foundation was to be the
There is a fundamental problem with the psychohistory concept; the
psychohistorians become the rulers and they, too, are human. Michael
Flynn makes it all clear in IN THE COUNTRY OF THE BLIND. Asimov didn't
come to terms with the issue in the Foundation trilogy; later on, in
FOUNDATION'S EDGE he confronted it but his solution was icky.
[Provided by Richard Harter [firstname.lastname@example.org]. There may be an updated
version at http://www.tiac.net/users/cri/asimov.html.]