This list includes only the actual books – much of the content is actually short stories (the volumes this is the case for are noted below). If you want a thorough accounting of which stories occur in what order, down to a listing of what years they occur in, I recommend Johnny Pez’s Insanely Complete Fiction List for a more detailed reading order.

The Robots Era:

I, Robot: To Protect
Novel set in 2035 featuring Susan Calvin and early robots, written by Mickey Zucker Reichert.
I Robot: To Obey
Novel set in 2036 featuring Susan Calvin and early robots, written by Mickey Zucker Reichert.
I, Robot: To Preserve
Novel set in 2037 featuring Susan Calvin and early robots, written by Mickey Zucker Reichert.
The Complete Robot
Contains all of Asimov’s Robot Stories up to the date of its publication.
Robot Dreams
Contains additional Robot short stories by Asimov.
Robot Visions
Contains additional Robot short stories by Asimov.
Gold
Contains additional Robot short stories by Asimov.
Predator
Volume 1 of the Robots in Time series by William F. Wu.
Marauder
Volume 2 of the Robots in Time series by William F. Wu.
Warrior
Volume 3 of the Robots in Time series by William F. Wu.
Dictator
Volume 4 of the Robots in Time series by William F. Wu.
Emperor
Volume 5 of the Robots in Time series by William F. Wu.
Invader
Volume 6 of the Robots in Time series by William F. Wu.
The Positronic Man
Novel length expansion of Asimov’s short story The Bicentennial Man, co-written with Robert Silverberg.
Nemesis
Novel by Asimov.
The Caves of Steel
First novel in the Elijah Baley series.
The Naked Sun
Second novel in the Elijah Baley series.
The Robots of Dawn
Third novel in the Elijah Baley series.
Odyssey
Volume 1 of the Robot City series written by Michael P. Kube-McDowell.
Suspicion
Volume 2 of the Robot City series written by Mike McQuay.
Cyborg
Volume 3 of the Robot City series written by William F. Wu.
Prodigy
Volume 4 of the Robot City series written by Arthur Byron Cover.
Refuge
Volume 5 of the Robot City series written by Robert Chilson.
Perihelion
Volume 6 of the Robot City series written by William F. Wu.
Changeling
Volume 1 of the Robot City: Robots and Aliens series written by Stephen Leigh.
Renegade
Volume 2 of the Robot City: Robots and Aliens series written by Cordell Scotten.
Intruder
Volume 3 of the Robot City: Robots and Aliens series written by Robert Thurston.
Alliance
Volume 4 of the Robot City: Robots and Aliens series written by Jerry Oltion.
Maverick
Volume 5 of the Robot City: Robots and Aliens series written by Bruce Bethke.
Humanity
Volume 6 of the Robot City: Robots and Aliens series written by Jerry Oltion.
Mirage
Novel written by Mark W. Tiedemann.
Chimera
Novel written by Mark W. Tiedemann.
Aurora
Novel written by Mark W. Tiedemann.
Have Robot, Will Travel
Novel written by Alexander C. Irvine.

The Empire Era:

Robots and Empire
Novel by Asimov.
Caliban
Novel written by Roger MacBride Allan.
Inferno
Novel written by Roger MacBride Allan.
Utopia
Novel written by Roger MacBride Allan.
The Stars, Like Dust
Novel by Asimov.
The Currents of Space
Novel by Asimov.
Pebble in the Sky
Novel by Asimov.

The Foundation Era:

Prelude to Foundation
Novel by Asimov.
Foundation’s Fear
Written by Gregory Benford. First novel in the Second Foundation trilogy.
Forward the Foundation
Novel by Asimov.
Foundation and Chaos
Written by Greg Bear. Second novel in the Second Foundation trilogy.
Foundation’s Triumph
Written by David Brin. Third novel in the Second Foundation trilogy.
Foundation
Novel by Asimov.
Foundation and Empire
Novel by Asimov.
Second Foundation
Novel by Asimov.
Foundation’s Edge
Novel by Asimov.
Foundation and Earth
Novel by Asimov.
Nightfall
Novel length expansion of the Asimov short story of the same name, co-written with Robert Silverberg. Although originally separate from the rest of the Asimov Universe, it was brought in by Kingsbury’s Psychohistorical Crisis, and placed here as it cannot fit anywhere before the fall of the Empire.
Foundation’s Friends: Stories in Honor of Isaac Asimov
Anothology of stories in the Asimov Universe written by other authors. Although the stories take place all across this timeline, they are mostly expansions of Asimov stories rather than integral parts of the series, and can thus best be read here. One story in this volume crosses over with The Stainless Steel Rat Timeline.
Psychohistorical Crisis
Novel by Donald Kingsbury. Although not an official sequel, it is clearly derived from the Foundation series. As noted above, it also brings in the story of Nightfall.
The End of Eternity
Novel by Asimov.