Asimov's robot stories comprise a far less coherent body of work than his Foundation series. The vast majority of them are short pieces with little in common with each other save the presence of robots. Even so, his mastery of world-building provided his readers with an easily grasped theoretical underpinning for the robot stories, such that his many compilations still hang together thematically.
The robots in Asimov's stories all behave according to a set of rules, formally introduced in his 1942 story "Runaround"--his "Three Laws of Robotics": 1. A robot may not injure a human being or, through inaction, allow a human being to come to harm. 2. A robot must obey orders given it by human beings except where such orders would conflict with the First Law. 3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law. A "Zeroth" law was added much later to account for some robotic actions not quite sensible under the 3 original laws: 0. A robot may not harm humanity, or, by inaction, allow humanity to come to harm. (The original laws were thereupon adjusted to conform to this heretofore implicit zeroth law.)
As in the Foundation series, Asimov's interests in the inner workings of philosophy, though, whether human or robotic, merely serve to provide the rational underpinnings for explorations of the human condition. His robot stories, paradoxically, contain his most emotionally affecting storylines and characterizations.
In the 1950s, Asimov wrote his lengthiest treatment of robots in a series of novels that resembled nothing so much as a series of mysteries. The central character, a robot named R. Daneel Olivaw, is shown to be the culmination of robot technology, and indeed, Asimov uses Olivaw in his final two Foundation novels (which were among the last of his writings) as well. This surprising, and quite unforeseeable, tying together of his two previously completely separate bodies of literature provided a neat final twist to his life's work.
Robot collections available from GPL:
R. Daneel Olivaw stories: