This is not a complete list of books that have been suggested, but it does have some of the more often-requested titles.
All copyright info is my understanding of it, as it applies to LibriVox but I am not a lawyer, so please use this as guidance and do your own checking if desired. Also, it is all current as of January 2019, but that's not to say the law in the US won't change again.

Books by Agatha Christie -- only her first three books, The Mysterious Affair at Styles, The Secret Adversary, and The Murder on the Links are in the US public domain. The first two have been recorded for LibriVox, but her estate disputed the legality of that, since the site was founded (and the domain name owned) by a Canadian. Christie's estate had taken an issue with this technicality and approached Hugh (the founder of LV). LV was threatened with legal action at the time if we did not remove the recordings -- even though the files were stored in the US, as all our files are, at archive.org. Since Christie died in 1976, her works will be PD in Canada at the start of 2027, and LibriVox should be safe at that point to record all her works published before 1932 (because US copyright law is in play too, of course -- covering everything published 95+ years before 2027.)
1984 by George Orwell
First published in 1949, US copyright will expire in 2045. (Because Orwell died in 1950, this book is already out of copyright in some countries, including Canada and Australia. See link above for more about LibriVox geography, though!)
Animal Farm by George Orwell
First published in 1945, US copyright will expire in 2041.
Anne of Ingleside by Lucy Maud Montgomery
First published in 1939, copyright later renewed, US copyright will expire in 2035.
Anne of Windy Poplars by Lucy Maud Montgomery
First published in 1936, copyright later renewed, US copyright will expire in 2032.
Apache Wedding Prayer (poem) by Albert Maltz
Usually thought to be a traditional prayer, this poem has been written by Albert Maltz for the movie Broken Arrow, in 1950.
Anne of Windy Poplars by Lucy Maud Montgomery
First published in 1936, US copyright will expire in 2032.
Atlas Shrugged by Ayn Rand
First published in 1957, US copyright will expire in 2053.
Blue Castle by Lucy Maud Montgomery
First published in 1926, copyright renewed in 1954, US copyright will expire in 2022.
Brave New World by Aldous Huxley
First published in 1932, US copyright will expire in 2028.
The Catcher in the Rye by JD Salinger
First published in 1951, copyright later renewed, US copyright now expires in 2044.
Cheaper By The Dozen by Frank Bunker Gilbreth, Jr. and Ernestine Gilbreth Carey
First published in 1948, copyright later renewed, US copyright now expires in 2044.
The Devil and Daniel Webster by Stephen Vincent Benet
First published in 1938, copyright later renewed, US copyright now expires in 2034.
Feynman Lectures On Physics by Richard Phillips Feynman
First published in 1962 (or 64?), copyright later renewed, US copyright now expires in 2058 (or 60).
The Fountainhead by Ayn Rand
First published in 1943, US copyright will expire in 2039.
The Four Quartets by T.S. Eliot
First published in 1943 and copyright renewed 1970. US copyright will expire in 2039. [Added by admin RuthieG]
Free Culture by Lawrence Lessig
First published in 2004, released electronically by the author under a Creative Commons license. US copyright expires 70 years after the death of the author. Note: It is available in audio format at achive.org: http://www.archive.org/details/free-culture-audiobook
Galactic Derelict by Andre Norton
First published in 1959, copyright later renewed, US copyright now expires in 2055. Author died in 2005, life+50 copyright expires in 2056 and life+70 expires in 2076.
The Godfather by Mario Puzo
First published in 1969, copyright later renewed, US copyright now expires in 2065.
Gospel of Judas
http://news.yahoo.com/s/nm/20060406/ts_nm/religion_judas_dc_2
Although this is an old document, the newly-published translations will be copyrighted, and so cannot be recorded here at LV until 70 years after the death of their translator.
The Gulag Archipelago, by Aleksandr Solzhenitsyn
First published in 1973, US copyright will expire in 2069. (Translations published between '73 and '77 expire 95 years after publication date. Translations published in and after 1978 will be in the public domain until life of translator + 70 years. )
Holidays on Ice, by David Sedaris
First published in 1997, US copyright on this work will expire on Jan. 1 70 years after the death its the author.
Imajica by Clive Barker
First published in 1991, US copyright will expire 70 years after the death of its author.
To Kill a Mockingbird by Harper Lee
First published in 1960, copyright later renewed, US copyright will expire in 2056.
Lady Chatterly's Lover by D.H. Lawrence
First published in 1928, US copyright will expire in 2024.
Last and First Men by Olaf Stapledon
First published in 1930, US copyright will expire in 2026.
Little House on the Prairie by Laura Ingalls Wilder
First published in 1935, copyright later renewed, US copyright now expires in 2031.
The Little Prince or, Le Petit Prince by Antoine de Saint Exupéry
First published in 1943, US copyright in the French text will expire in 2039. No translations can be in the public domain until after that date.
The Magic Garden by Gene Stratton Porter First published posthumously in 1927, copyright later renewed, US copyright now expires in 2023.
The Notebook by Nicholas Sparks
First published in 1996, US copyright will expire 70 years after the death of its author.
Of Mice and Men by John Steinbeck
First published in 1937, US copyright will expire in 2033.
Oil, by Upton Sinclair
First published in 1927, copyright renewed 1954, US copyright expires 31 Dec 2022, will be Public Domain 1 Jan 2023.
Orlando, by Virginia Woolf
First published in 1928, copyright renewed 9 Nov 1955, US copyright expires 31 Dec 2023, will be Public Domain 1 Jan 2024.
Out of Africa, by Isak Dinesen
First published in the US in 1938, US copyright will expire in 2034.
Ovid's Metamorphoses translated by A. S. Kline
This can't be read at LibriVox because we release all our recordings into the public domain -- that means there are no limitations on the uses people can put them to ... including selling them commercially, which conflicts with the 'Creative Commons' license used by the translator. This particular translation will enter the public domain 70 years after the death of its translator. Older translations are recordable, for example, here.Copyright 2000, All Rights Reserved
This work MAY be FREELY reproduced, stored and transmitted, electronically or otherwise, for any NON-COMMERCIAL purpose.
The Pearl by John Steinbeck
First published in 1947, Copyright renewed in 1974. US copyright will expire in 2043.
The Phantom Tollbooth by Norton Juster
First published in 1961, US copyright will expire in 2057.
Precious Bane: A Novel by Mary Webb
First published in 1924 outside the US, published in the US in 1926, US copyright will expire in 2022.
The Quiet American by Graham Greene
First published in 1955, US copyright will expire in 2051.
A Roving Commission by Winston Spencer Churchill
First published in 1930, copyright later renewed, US copyright now expires in 2026.
The Stranger, or The Outsider, or L’Étranger by Albert Camus
First published in 1942, US copyright in the French text will expire in 2038. No translations can be in the public domain until after that date.
The Trial (English translation) by Franz Kafka
The first English translation was done by Willa & Edwin Muir in 1937. That edition's copyright will expire in 2033.
The version on Project Gutenberg is copyrighted.
We the Living by Ayn Rand
First published in 1936, copyright later renewed, US copyright now expires in 2032.
West Side Story by Arthur Laurents
First published in 1957, copyright later renewed, US copyright now expires in 2053.
Books by Cory Doctorow -- although these are often released under Creative Commons licences, that still limits what can be done with the file and is not the same as being in the Public Domain. 70 years after author's death, unless he puts them into the PD before that.
Books by Stephen King -- enter the public domain 70 years after author's death.