I read in another answer that Fox produced the film I, Robot because they had just acquired the rights to the Asimov collection and wanted to get a big budget movie out of it. I would have thought his books are old enough to already be in the public domain, but obviously I'm not very familiar with the law. When does the copyright expire on his various works?
There are various terms for US copyright and when the works published in that situation nominally expire.
However, since the 1980s every 20 years a new copyright extension act that includes all works published in a range including 1928 has been passed by the US congress.
This is because Steamboat Willy was published in 1928, the first appearance of Mickey Mouse. Disney forcefully lobbies for a 20 year extension every 20 years.
The next due date is 2023, so we should expect a new copyright extension act to miraculously appear and pass the US house and senate in the next 5 years.
As all of Dr Asimov's works where published after Steamboat Willy, we should expect his works to remain under copyright (at least in the USA) indefinitely, regardless of what the current law states.
Outside of the USA, it is a regular demand of the USA in trade treaties to include copyright extension on the part of the other party. Historically there have been gaps, but they haven't been commercially significant.
As the expiery of century-old works is not a hot button issue for people who don't own century-old works, it is very difficult to defeat the concentrated lobbying power and regulatory capture.
See this article for a more in-depth take on the issue.
Under current law, it lasts 95 years from date of publishing or 70 years from death. Which, as noted, doesn't mean anything of substance.
This question is covered by the Asimov FAQ:
All of Asimov's work, fiction and non-fiction, was under copyright at the time of the Good Doctor's death. Under current U.S. law, the copyrights for his works published before 1978 will not expire until 95 years after the copyrights were obtained, and those published from 1978 onward will remain in effect for 70 years after his death. Thus these copyrights will remain in effect until dates ranging from 2034 (for his first story published in 1939), through 2072 (for works published in 1977), and works published from 1978 onward will remain under copyright until 2062, although the relevant laws may change between now and then.
(emphasis is mine)
Addendum: User Thunderforge correctly pointed out that the OP specifically mentioned I, Robot, so here is some additional information. As mentioned by Thunderforge, I, Robot was published in 1950, which implies a copyright until 2045. However, most of the stories in this collection were first published a few years before they were collected, so their copyright expires a few years earlier:
Story First published Copyrighted until ======================= =============== ================= Robbie 1940 2035 Runaround 1941 2036 Reason 1941 2036 Catch That Rabbit 1944 2039 Liar! 1941 2036 Little Lost Robot 1947 2042 Escape! 1944 2039 Evidence 1946 2041 The Evitable Conflict 1950 2045 (I, Robot frame story) 1950 2045
In his autobiography Asimov specifically mentions making sure to renew the copyright on each of his works as the expiration date came up, and how this became more and more of an chore as his body of work increased. If I recall correctly, he has more than 500 books credited to have written or edited.
I don't know, but I would assume that his estate (probably his daughter?) makes a point of looking after copyright renewals, and that you should not expect any of his works to end up in the public domain any time soon.